Optimization of the Production Process of Lallemand Ibéria ... · Supervisors: Prof. Paulo José da Costa Branco ... Then I thank Eng. Sandro Ratinho, ... 3 1.3 OBJECTIVES

Optimization of the Production Process of Lallemand

Ibéria SA to Reduce Electric Energy Costs Using a

Genetic Algorithm

Diogo Correia Amado

Thesis to obtain the Master of Science Degree in

Electrical and Computer Engineering

Supervisors: Prof. Paulo José da Costa Branco

Prof. Susana Margarida da Silva Vieira

Examination Comitee

Chairperson: Prof. Rui Manuel Gameiro de Castro

Supervisor: Prof. Susana Margarida da Silva Vieira

Members of the Comitee: Prof. Pedro Manuel Santos de Carvalho

March 2015

II

III

Acknowledgements

First of all, I want to thank my supervisor Professor Paulo Branco for his availability, willingness

to help and especially his friendship demonstrated during the realization of this thesis. Likewise,

I give my thanks to my co-supervisor Professor Susana Vieira for all the transmitted knowledge

and disposition to always help.

A great word of affection goes to my family, especially my mother and father, who are always

there for me and do everything for my happiness.

I thank Galp for the excellent initiative to bring closer university students and the industrial world.

Then I thank Eng. Sandro Ratinho, as Lallemand Iberia SA CEO, for embracing this project and

give me the opportunity to perform a work with such practical applications inserted in the

company.

I want also to thank Eng. Henrique Cabaceira and Eng. Ana Maria Pinto for their support while I

was in the company and for all their interest and concern about my well-being and my activities

developed during the internship.

A special “thank you” to Eng. Vasco Catarino for his friendship and for accompanying and helping

me in every moment of this project.

I must thank all employees in Lallemand who were always kind and ready to assist me in any way

they could.

And a warm thanks I give to all my friends for their companionship and motivation given in the

course of this thesis, plus the great moments they always provide and helped me distract from

work time to time.

To them all, thank you.

IV

V

Abstract Lallemand Ibéria S.A. is a yeast producing company and great part of its expenses come from

electric energy. Therefore it is important search for inefficient energy practices and look for

possible solutions to solve them. The fermentation process of the company is one of the areas

that has the potential to see their energy consumption costs reduced and it will be the focus of

this thesis. Yeast development is guaranteed by adding nutrients, treacle and by pumping air into

the fermenters with the help of air compressors. The fermentations follow weekly plans made

manually by the production manager and, since he does not take into account the different periods

present in the electric tariff, sometimes peak consumption coincides with super peak hours,

greatly increasing the energy costs. Plus, the company has not done any research in what should

be the best tariff to contract. Therefore, given the complexity of the problem, the whole process

was characterized and modelled into a simulation program, which also has a genetic algorithm.

By using this program the company can decrease electric energy expenses, moreover when there

is no investment cost besides the optimization program. Savings are reached if Lallemand

switches from the current contracted tariff (weekly cycle) to the tariff with the optional weekly cycle

and those savings will be even higher if the optimization algorithm is used to optimize the weekly

production plans.

Keywords

Energy efficiency; power consumption; electric energy tariffs; process modelling; genetic

algorithm; problem optimization.

VI

Resumo A Lallemand Ibéria S.A. é uma empresa que produz fermento e grande parte das suas despesas

advém do consumo de energia eléctrica. Por isso é importante procurar por práticas que são

ineficientes do ponto de vista energético e encontrar soluções para as corrigir. O processo de

fermentação presente na empresa é uma das áreas que tem potencial para que os seus custos

com a energia sejam reduzidos e foi precisamente nesta área que se focou esta tese. O

crescimento da levedura neste processo é assegurado pela adição de melaço, nutrientes e pela

bombagem de ar através de compressores aos 5 fermentadores existentes. As fermentações

seguem um plano semanal efectuado manualmente pelo responsável de produção (plano de

fábrica) e uma vez que este não tem em conta os diferentes períodos horários presentes na tarifa

eléctrica, muitas vezes os picos de consumo dão-se nas horas de ponta, aumentando muito os

custos ligados à energia eléctrica. Para além disso, a Lallemand há muito tempo que não

averigua qual é a tarifa que melhor se insere nos gastos da empresa. Por isso, dada a

complexidade do problema, caracterizou-se e modelou-se todo o processo de fermentação para

usar num programa de simulação que também contém um algoritmo genético. Ao adoptar este

programa a empresa pode reduzir os seus gastos com a energia eléctrica. A poupança é

alcançada ao trocar a tarifa actual contratada (ciclo semanal) pela tarifa com o ciclo semanal

opcional e ao aplicar o algoritmo de optimização nos planos semanais de produção.

Palavras-chave

Eficiência energética; consumo de energia; tarifas eléctricas; modelação de processos; algoritmo

genético; optimização de problemas.

VII

Index

LIST OF FIGURES ..................................................................................................................................... IX

LIST OF TABLES ........................................................................................................................................ X

LIST OF SYMBOLS .................................................................................................................................. XII

1 INTRODUCTION ................................................................................................................................ 1

1.1 FRAMEWORK AND MOTIVATION ........................................................................................................ 2

1.2 LALLEMAND IBÉRIA S.A. .................................................................................................................. 3

1.3 OBJECTIVES .................................................................................................................................. 3

1.4 STRUCTURE AND ORGANIZATION ....................................................................................................... 3

2 CHARACTERIZATION OF THE PRODUCTION PROCESS ...................................................................... 5

2.1 FERMENTATION ............................................................................................................................. 6

2.2 AIR CONSUMPTION......................................................................................................................... 8

2.3 POWER CHARACTERIZATION OF THE COMPRESSORS ............................................................................. 11

2.3.1 Aerzen compressors ......................................................................................................... 11

2.3.2 Turbo compressors .......................................................................................................... 12

2.3.3 Holmes compressors ........................................................................................................ 14

2.3.4 Separators ....................................................................................................................... 15

3 PORTUGUESE TARIFF SYSTEM ........................................................................................................ 16

3.1 OVERVIEW ................................................................................................................................. 17

3.2 LALLEMAND CONTRACTED TARIFF .................................................................................................... 18

4 PROBLEM IDENTIFICATION ............................................................................................................ 21

5 MATHEMATICAL FORMULATION OF THE PROBLEM ...................................................................... 24

5.1 DECISION VARIABLES .................................................................................................................... 25

5.2 ENERGY CONSUMPTION MODELLING ................................................................................................ 26

5.2.1 Aerzen Compressors Energy Consumption ....................................................................... 26

5.2.2 Turbo Compressors T1 and T2 Energy Consumption ......................................................... 27

5.2.3 Holmes Compressors Energy Consumption ...................................................................... 29

5.3 ENERGY COSTS MODELLING ............................................................................................................ 30

5.4 OBJECTIVE FUNCTION ................................................................................................................... 33

VIII

5.5 CONSTRAINTS ............................................................................................................................. 33

5.5.1 Resources Constraints ...................................................................................................... 34

5.5.2 Production needs constraint ............................................................................................ 35

5.5.3 Time constraint ............................................................................................................... 36

6 IMPLEMENTATION OF THE GENETIC ALGORITHM.......................................................................... 37

6.1 GENETIC ALGORITHM ................................................................................................................... 38

6.2 MATLAB GLOBAL OPTIMIZATION TOOLBOX – GENETIC ALGORITHM ........................................................ 39

6.3 PARAMETERS OF GENETIC ALGORITHM ............................................................................................. 40

6.3.1 Selection .......................................................................................................................... 40

6.3.2 Elitism ............................................................................................................................. 40

6.3.3 Crossover ......................................................................................................................... 41

6.3.4 Mutation ......................................................................................................................... 41

6.4 IMPLEMENTATION OF THE GENETIC ALGORITHM TO THE OPTIMIZATION PROBLEM ...................................... 42

6.4.1 Encoding and Decoding ................................................................................................... 42

6.4.2 Parameters Values of the Genetic Algorithm ................................................................... 42

7 RESULTS ......................................................................................................................................... 46

7.1 FACTORY PLAN VS OPTIMIZED PLAN WITH WEEKLY CYCLE ....................................................................... 50

7.2 RESULTS WITH THE OPTIONAL WEEKLY CYCLE ...................................................................................... 54

7.3 SIMULATED OPTIMIZED PLANS VS TESTED OPTIMIZED PLANS ................................................................... 57

8 CONCLUSIONS AND PROSPECTIVE WORK ...................................................................................... 61

8.1 CONCLUSIONS ............................................................................................................................. 62

8.2 PROSPECTIVE WORK ..................................................................................................................... 64

REFERENCES ........................................................................................................................................... 65

APPENDIX A ........................................................................................................................................... 66

AERZEN GM 90S CHARACTERISTICS CATALOGUE ............................................................................................ 66

APPENDIX B ........................................................................................................................................... 67

POWER MEASUREMENTS WITH THE FLUKE 1735 POWER ANALYSER .................................................................... 67

APPENDIX C............................................................................................................................................ 68

STRUCTURE OF THE SIMULATION PROGRAM ................................................................................................... 68

GUI ..................................................................................................................................................... 71

IX

List of figures

Figure 1 - Production process ......................................................................................................7

Figure 2 - Fermenters F1, F2, F3, F4 and F5 ...............................................................................8

Figure 3 - Average air consumption profile in F1 ..........................................................................9





Figure 8 - Fermenters and compressors connection scheme.....................................................10

Figure 9 - Power consumption as a function of air flow volume in each Aerzen compressor .....12

Figure 10 - Power consumption as a function of air flow for T1 ..................................................13

Figure 11 - Power consumption as a function of air flow for T2 ..................................................13

Figure 12 - Turbo 1 .....................................................................................................................14

Figure 13 - Turbo 2 .....................................................................................................................14

Figure 14 - Holmes 1 and Holmes 2 ...........................................................................................15

Figure 15 - Separators ...............................................................................................................15

Figure 16 - Access Tariffs for the liberalised market – adapted from [5] ....................................17

Figure 17 - Resources profile: (a) availability, (b) utilization and (c) feasibility – adapted from [1]

...................................................................................................................................................34

Figure 18 - Genetic algorithm basic cycle – adapted from [3].....................................................39

Figure 19 - Comparison of energy consumption between the factory plan and the optimized plan

with weekly cycle in week 1 ........................................................................................................51











Figure 25 - Power consumption in week 2: simulation results vs real results for T1...................59

Figure 26 - Power consumption: simulation results vs real results for T2 ...................................59

Figure 27 - T1 power consumption from 24 to 29 of April ...........................................................67

Figure 28 – T2 power consumption from 24 to 29 of April ..........................................................67

Figure 29 - Structure of the program ..........................................................................................68

X

List of tables Table 1 - Fermentation duration and output of each fermenter ....................................................7

Table 2 – Matching points between power consumption and air flow volume in each Aerzen

compressor.................................................................................................................................11

Table 3 - Characteristics of the Turbo compressors ...................................................................12

Table 4 - Weekly cycle hourly periods ........................................................................................19

Table 5 - Optional weekly cycle hourly periods ..........................................................................20

Table 6 - Integer and binary variables for each fermenter ..........................................................25

Table 7 – Approximate mode of turning on and off T1 and T2 depending on the air volume in the

collector ......................................................................................................................................28

Table 8 - Performance of the optimization algorithm for several parameters combinations for test

1 .................................................................................................................................................44


2 .................................................................................................................................................44


1 .................................................................................................................................................45

Table 11 - Selected values for the parameters of the genetic algorithm .....................................45

Table 12 - Minimum time for the 1st fermentation to start in each fermenter in week 1 ..............47

Table 13 - Factory plan with contracted weekly cycle in week 1 ................................................47











Table 24 – Results of the optimized plan compared to the factory plan with weekly cycle in week

1 .................................................................................................................................................51

Table 25 - Results of the optimized plan compared to the factory plan with weekly cycle in week

2 .................................................................................................................................................51


3 .................................................................................................................................................52


4 .................................................................................................................................................52

XI


5 .................................................................................................................................................53


6 .................................................................................................................................................53

Table 30 – Results of the factory and optimized plan with optional weekly cycle compared to the

factory plan with weekly cycle in week 1 ....................................................................................55











Table 36 - Electric energy costs in the first 8 months of 2014 for the two different tariff cycles:

weekly cycle and optional weekly cycle ......................................................................................57

Table 37 - Test and simulation results using the optimized plan in week 2: comparison and

deviation .....................................................................................................................................58

XII

List of symbols EU – European Union

F1 – Fermenter 1

F2 – Fermenter 2

F3 – Fermenter 3

F4 – Fermenter 4

F5 – Fermenter 5

A1.1 and A1.2 – Aerzen compressors pumping air into F1

A2.1 and A2.2 – Aerzen compressors pumping air into F2

T1 – Turbo 1

T2 – Turbo 2

H1 – Holmes 1

H2 – Holmes 2

SEN – National Electric System

ERSE – Regulatory Entity of the Energy System

i – Number of the fermentation

𝑥𝑖 – Integer decision variable

𝑥𝑖+36 – Binary decision variable

𝐸𝑡𝑜𝑡𝑎𝑙 – Total energy consumption in each time interval [kWh]

𝐸𝐴1 – Energy consumption in each Aerzen feeding F1 in each time interval [kWh]

𝐸𝐴2 – Energy consumption in each Aerzen feeding F2 in each time interval [kWh]

𝐸𝑇1 – Energy consumption by Turbo T1 in each time interval [kWh]

𝐸𝑇2 – Energy consumption by Turbo T2 in each time interval [kWh]

𝐸𝐻1 – Energy consumption by Holmes H1 in each time interval [kWh]

𝐸𝐻2 – Energy consumption by Holmes H2 in each time interval [kWh]

𝑎𝑖𝑟𝐴𝑒𝑟𝑧𝑒𝑛 – Air consumed by each Aerzen compressor in each time interval [m3/h]

𝐹𝑎𝑖𝑟𝐴𝑒𝑟𝑧𝑒𝑛 – Air consumption given a scheduled plan in each time interval for each Aerzen

compressor [m3/h]

XIII

𝑥 – Scheduled weekly plan

𝑡 – Discrete time variable

𝑃𝐴𝑒𝑟𝑧𝑒𝑛 – Power consumed by each Aerzen compressor as a function of pumped air volume [kW]

Δ𝑡 – Power integration constant

𝑎𝑖𝑟𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟 – Air injected into the collector in each time interval [m3/h]

𝐹𝑎𝑖𝑟𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟 – Air injected into the collector given a scheduled plan in each time interval [m3/h]

𝑎𝑖𝑟𝑇1 – Air pumped by Turbo T1 in each time interval [m3/h]

𝐹𝑎𝑖𝑟𝑇1 – Air pumped by Turbo T1 given a scheduled plan in each time interval [m3/h]

𝑎𝑖𝑟𝑇2 – Air pumped by Turbo T2 in each time interval [m3/h]

𝐹𝑎𝑖𝑟𝑇2 – Air pumped by Turbo T2 given a scheduled plan in each time interval [m3/h]

𝑃𝑇1 – Power consumed by Turbo T1 as a function of pumped air volume [kW]

𝑃𝑇2 – Power consumed by Turbo T2 as a function of pumped air volume [kW]

T1s – Status of Turbo T1 in each time interval


𝐹𝑇1 – Binary function indicative of Turbo T1 status depending on the air consumed by the collector

in each time interval



𝐻1𝑠 – Status of H1 (on or off)

𝐹𝐹1 – Binary function indicating if F1 is in the fermentation stage given a certain scheduled plan,


𝐻2𝑠 – Status of H2



𝑃𝐻1 – Nominal power of H1

𝑃𝐻2 – Nominal power of H2

𝐻𝑆𝑝 – Binary function indicating the time intervals corresponding to Super peak hours

𝐻𝑝 – Binary function indicating the time intervals corresponding to peak hours

𝐻𝑆𝑜𝑓𝑓 – Binary function indicating the time intervals corresponding to Super off-peak hours

𝐻𝑜𝑓𝑓 – Binary function indicating the time intervals corresponding to off-peak hours

XIV

𝑐𝑆𝑝𝑎 – Active energy cost in Super peak hours [€/kWh]

𝑐𝑝𝑎 - Active energy cost in peak hours [€/kWh]

𝑐𝑆𝑜𝑓𝑓𝑎 - Active energy cost in Super off-peak hours [€/kWh]

𝑐𝑜𝑓𝑓𝑎 - Active energy cost in off-peak hours [€/kWh]

𝑐𝑆𝑝𝑛 – Energy network access cost in Super peak hours [€/kWh]

𝑐𝑝𝑛 - Energy network access cost in peak hours [€/kWh]

𝑐𝑆𝑜𝑓𝑓𝑛 - Energy network access cost in Super off-peak hours [€/kWh]

𝑐𝑜𝑓𝑓𝑛 - Energy network access cost in off-peak hours [€/kWh]

𝑐𝑐𝑝 – Cost per kW of contracted power day [€/kWday]

𝑐𝑆𝑝𝐻 – Consumed power in super peak hours cost [€/kWday]

𝑁𝑆𝑝𝐻 – Number of super peak hours in one week

𝑐𝑡𝑎𝑥 – Special tax over electricity consumption

𝐸𝑆𝑝𝐻 – Energy consumed in Super peak hours

𝐸𝑝𝐻 – Energy consumed in peak hours

𝐸𝑆𝑜𝑓𝑓𝐻 – Energy consumed in Super off-peak hours

𝐸𝑜𝑓𝑓𝐻 – Energy consumed in off-peak hours

𝐶 – Total electric energy consumption cost for a certain scheduled plan x

Y – Ton of yeast produced for a certain scheduled plan x

𝐹𝑜𝑏𝑗𝑒𝑡𝑖𝑣𝑒 – Objective function

𝑁𝐹𝑘 – Number of scheduled fermentations in fermenter k

𝑈𝑠𝑒𝑝 – Difference between availability and utilization profiles for a given plan

𝑌𝐵 – Quantity of type B yeast produced for a given plan

B – Quantity of type B yeast required

𝑜𝑢𝑡 – Output of each fermenter in each scheduled fermentation

𝑌𝐴 – Quantity of type A yeast produced for a given plan

A – Quantity of type A yeast required

𝑇𝐹𝑘 – Fermentation time in fermenter k

GUI – Graphical User Interface

1 Introduction

2

1.1 Framework and Motivation

The growing concern in increasing equipment efficiency and promoting efficient practices, either

for households or industries, is a reality. In fact, energy efficiency is one of the “20-20-20” targets

of Europe Union, which aims to improve it by 20%, along with a 20% reduction of greenhouse

gas emissions from 1990 levels and a 20% consumption of renewable energy in the total energy

consumption in 2020 [1]. Therefore, it is very important to raise awareness for this matter and

invest and implement efficiency measures in order to help EU meet these targets. Moreover, by

increasing efficiency, households and industries will harvest the inherent benefits and will see

their energetic expenses reduced.

Particularly, in many industries the biggest expenses come from their electric energy

consumption. There, production processes can be complex and improving efficiency is more than

replacing old equipment for new equipment with higher levels of efficiency. It is also important to

characterize those internal production processes in order to evaluate their performance and look

for inefficiencies that can be solved, thus reducing costs and maximizing overall energy efficiency.

The use of optimization algorithms for the modelled production processes is an effective way to

obtain better production solutions in energy and costs terms. However, sometimes the processes

are too complex to represent and optimize via conventional math programming. Instead, different

ways of optimization are needed to better suit these cases, such as heuristic methods [2].

Heuristic method is a procedure to find feasible and good solutions and it fits usually a specific

problem with a specific set of constraints and assumptions rather than a variety of problems [2][3].

Optimality and solution finding is not guaranteed, but it often requires less time than exact

methods [2]. Particularly, algorithms based on natural evolutionary process fit well a wide range

of problems in a multitude of fields, such as engineering. A genetic algorithm belongs to that class

of evolutionary algorithms and it is a search heuristic method that is based on the natural selection

processes present in biologic evolution, thus being a useful weapon to search efficiently in large

spaces [3].

Lallemand S.A. is a yeast producing company that consumes a lot of electric energy and has a

fermentation process requiring weekly scheduling that has a very large solutions space.

Therefore, it fits perfectly in the efficiency problem optimization and given its dimension and

complexity, after modelling the whole process, a genetic algorithm to create optimized weekly

plans will be used and put into test.

3

1.2 Lallemand Ibéria S.A.

Lallemand Ibéria S.A. initiated its industrial activity in 1973. The headquarters are located in

Setúbal, in the zone of Cachofarra, near Sado River. The activity of Lallemand is developed,

mainly, in the area of biotechnology, producing yeast, live microorganisms from the species

Saccharomyces cerevisae. Its commercialization is made under the form of cream yeast, pressed

yeast and dry yeast, which are used in bakery and pastry industries. The company has

approximately 60 employees and works uninterruptedly, 24 hours per day, 7 days per week.

The investment in new technologies and equipment, the continuous improving and research and

development constitute the bases for the success of Lallemand that exports for all over the world

around 70% of its production. The remaining 30% are sold in the Portuguese market.

A complete fermentation cycle is constituted by the fermentation, separation and initialization

processes, and its production plans are made on a weekly basis by the responsible production

manager.

1.3 Objectives

As seen in the two previous sections, Lallemand is a yeast producing company that has a

fermentation process planned in a weekly basis. Those plans depend on the production needs

and are created by the production manager. The main goal of this thesis is to reduce the energy

costs per ton of yeast produced. Hence, it is necessary modelling all the production process first.

Then, within this main goal, several objectives are to be accomplished: creation of a simulation

program with the model of the fermentation process and an optimization algorithm to lessen its

electric energy costs, since the weekly planning performed by the production manager does not

take into account the energy price variation over one day; ascertainment of what electric tariff is

economically better for the company and, finally, identification and searching for solutions for

another inefficiencies present in the process.

1.4 Structure and Organization

After defining the objectives, this master thesis is organized in 8 chapters. The first and the last

represent the introduction and conclusions, respectively. In chapter 2 the whole fermentation

process is going to be described, where air consumption of the fermenters and power

consumption of the machines are going to be characterized. In chapter 3 a general insight about

the Portuguese electric tariff system will be given, with special emphasis on the tariffs that are

possible to contract by Lallemand. In chapter 4 the problems present in the company will be

4

identified, and these are the problems that will be considered for electric costs reduction. In

chapter 5 the fermentation process is going to be mathematically modelled: decision variables for

the optimization problem will be defined, the power characteristics of the machines as a function

of air consumption and the energy costs of the tariff will be represented, the objective function is

going to be formulated and the constraints for the problem will be identified. In chapter 6 the

genetic algorithm used in the program will be fully described and its parameters will be chosen to

appropriately suit this specific scheduling problem of Lallemand. Finally, in chapter 7 the results

will be presented. Results for the factory and optimized plans given different tariffs for the

fermentation process, energy costs in the whole company given different tariffs and practical tests

results.

In short, in chapters 2 and 3 it will be characterized the production process and the Portuguese

electric tariff, then in chapters 4 and 5 it will be identified the problems related to energy costs and

efficiency and it will be modelled all the production process and finally, in chapter 6 the used

genetic algorithm will be explained

5

2 Characterization of

the production

process

6

2.1 Fermentation

To obtain one of the final three products (cream yeast, pressed yeast or dry yeast) there are

several stages yeast needs to go through. Firstly, the company receives pure cultures of the

lineage Saccharomyces cerevisae non-modified genetically. Then a pure culture is inserted in a

fermenter (pure culture fermenter) which contains sterilized treacle and other nutrients such as

ammonia, diammonium phosphate, magnesium sulphate and vitamins. Specific air, pH and

temperature conditions are assured to this culture. When this pure culture reaches a certain level

of development it will be transferred to a main fermenter (fermenter F4), which is again fed in a

regular and continuous manner with treacle, nutrients and air, maintaining temperature and pH

conditions. Air compressors are responsible for keeping the needed air flow and the temperature

is controlled by pumping water from the river into a pipeline that cools down the fermenters

through a heat exchanger. Therefore the water does not contact with the product itself, returning

into the river in conditions similar to the ones before the pumping and according to legislation

parameters.

In the end of this initial stage the resulting yeast (mother yeast) is distributed over another four

fermenters (F1, F2, F3 and F5) similar to the main fermenter to continue the production process.

After yeast gets fermented in each one of the 4 fermenters (commercial yeast) it goes directly to

the separators, where its cells are separated by centrifugation from the must where they grew up,

thus obtaining the first final product: cream yeast. This cream yeast is stored in refrigerated tanks

and it is dispatched in isothermal tank trucks. Pressed yeast is acquired by applying a rotating

vacuum filter to cream yeast. The resulting paste is extruded in order to form blocks which are

packed in carton boxes and stored in refrigerators until their dispatch. Lastly, dry yeast, like

pressed yeast, results from applying a rotating vacuum filter to cream yeast but after is also

submitted to a drying process until approximately 96% of dry matter is achieved. Dry yeast is

stored in silos before being packed through an automated process by vacuum, which is a

necessary condition to maintain the characteristics of this type of yeast.

After finishing the fermentation and separation processes and before initiating the next new

fermentation, every fermenter must be “initialized”, i.e. they go through a cleaning and preparation

process for the next fermentation. These three processes combined (fermentation, separation

and initialization) make the so-called fermentation cycle.

The whole production process is schematized in figure 1.

7

Figure 1 - Production process

As it was previously stated, there are three main stages in the production process: fermentation,

separation and initialization. Each fermenter has a certain duration associated to each one of

those stages, as well as a specific product quantity output. Table 1 shows the duration of the

processes and the output quantities concerning each fermenter. It must be noted that the

presented values are the ones used by the operators and the production manager to create the

weekly schedules, despite being average values that vary a little bit from fermentation to

fermentation.

Fermenter Yeast type Fermentation

[h] Separation

[h] Initialization

[h]

Total duration

[h]

Output [ton]

F1 Commercial 15 3,5 2,5 21 30

F2 Commercial 14 2,5 3,5 20 24

F3 Commercial 14 2,5 3,5 20 20,5

F5 Commercial 14 2,5 3,5 20 20,5

F4 Mother 24 2,5 3,5 30 20,5

Table 1 - Fermentation duration and output of each fermenter

8

Figure 2 - Fermenters F1, F2, F3, F4 and F5

2.2 Air consumption

To control the development of the yeast is necessary to assure specific air flow conditions, which

vary over the time of a fermentation cycle and are different in every fermenter. The air

consumption in each fermenter is registered by the responsible operators every hour, in m3/h,

and it follows a typical profile. However, it may differ from fermentation to fermentation due to

certain factors such as air humidity, air temperature, water temperature, technical problems that

sometimes happen and cannot be foreseen and also the fact that these values are registered

manually by the operators, which is liable to inaccuracies. Therefore it is important to gather all

the data regarding the air consumption in each fermenter over a certain period of time to perform

a statistical analysis to build an average typical profile for each of the 5 fermenters.

With that purpose, around 100 fermentations cycles, randomly picked between the years of 2013

and 2014, were used to obtain an average air consumption profile for each fermenter. As it was

mentioned before, the air consumption profile varies each fermentation. Nonetheless, this

variation is more evident in the absolute values of air consumption each hour rather than in their

relative difference from hour to hour, which is what will matter for the optimization algorithm, as it

will be seen in the upcoming chapters.

9

Figure 3 - Average air consumption profile in F1





In figures 4 to 7 it is shown the average air consumption profile for each fermenter. Figure 8 shows

that fermenters F1 and F2 are each one fed by two compressors called Aerzen (A1.1 and A1.2

feed F1; A2.1 and A2.2 feed F2), while the other three fermenters are connected to a common

collector fed by two compressors called Turbo 1 (T1) and Turbo 2 (T2). Air is injected into the

collector at a constant pressure of 800 mBar. The decision of turning ON and OFF these turbo

compressors is made manually by the operators respecting, however, a certain pattern related to

the air volume to be injected in the collector, as it will be explained in chapter 5. The overall

schematic for the air injection system is pictured in figure 8.

10

Figure 8 - Fermenters and compressors connection scheme

In figures 3 to 7, contrary to what should be expected, when the fermentation process is finished

in the fermenters, i.e. the process is in either the separation or initialization part, there is still air

being consumed. This air consumption is around 1000 m3/h and its only purpose is to avoid

bacteria and impurities entrance in the fermenters.

In fermenters F1 and F2 there are two small compressors that feed them when there is not any

fermentation happening. These compressors Holmes 1 (H1) and Holmes 2 (H2) are not

represented in figure 7. The air circulation for the other 3 fermenters when they are not having

any fermentation is done by availing the air present in the collector that is being used for other

fermentations. For example, if F3 does not have a fermentation going on but F4 and F5 do, F3

will demand the needed 1000 m3/h for air circulation from the collector by just slight increasing

the air injected by the Turbo compressors connected to the collector, which were already feeding

F4 and F5. If by any chance F3, F4 and F5 are not fermenting, which is a rare situation, both

Holmes can and will then feed the collector to assure air circulation in these 3 fermenters.

11

2.3 Power Characterization of the Compressors

2.3.1 Aerzen compressors

There are four equal Aerzen compressors (A1.1, A1.2, A2.1 and A2.2) that are linked to

fermenters F1 and F2 (two compressors for each of them). Hence, since each pair of compressors

feeds just one fermenter individually and independently, these compressors work almost always

very close to maximum power. Hence, for the program development it will be considered that the

power they consume is constant for each volume of air injected. This assumption is needed to

compare the simulation tests to the experimental ones in chapter 8, once power measurements

in working conditions were not made in the four Aerzen but they were done only in the two turbo

compressors. However, these Aerzen compressors are relatively new and as such it is reasonable

to associate the same certain power to the respective certain volume of air injected. Still it is

important to note this is an approximation. Also, both compressors of the same pair feeding each

fermenter consume the same power.

Each Aerzen compressor is referenced as GM 90S and works with an induction motor with

nominal power of 150 kW. Their power consumption characteristic can be taken directly from the

manufacturer catalogue, in Appendix A. By matching the power curves with the air flow curves

and the pressure curve of 800 mBar the following table is obtained:

Power (kW) Air flow volume (m3/h)

76 2700

84 3000

92 3300

100 3600

108 3900

116 4200

124 4500

132 4800

140 5100

148 5400

Table 2 – Matching points between power consumption and air flow volume in each Aerzen compressor

Now it is necessary to get an expression that represents the power consumption as a function of

air volume to be implemented in the simulation program. Using a simple linear regression the

following curve and consequent expression of power consumption (y) as a function of air flow (x)

come as indicated in figure 9:

12

Figure 9 - Power consumption as a function of air flow volume in each Aerzen compressor

2.3.2 Turbo compressors

Turbo 1 and Turbo 2 are the compressors that pump air into the collector, which it will feed F3,

F4 and F5 fermenters. As it was already written in section 2.2, the collector has always a constant

pressure of 800 mBar. The load seen by these Turbo compressors is established by varying the

angle of vanes at the exit of the compressors, thus changing the air volume that is injected into

the collector, which in turn alters the load torque exerted to the compressor. They also operate at

a constant speed of 2965 rpm.

Turbo 1 and Turbo 2 feed together 3 fermenters (F3, F4 and F5), therefore having a working point

dependent of the fermentations that are in progress and also their state (air consumption in each

fermentation). Since the weekly production plans are never the same, the operation of these

Turbo compressors is very variable and acyclic, contrary to the 4 Aerzen compressors.

In table 3 it is shown the characteristics of the motors of these two compressors, which are

referenced as HV-Turbo.

Motor Reference Type Power (kW)

Turbo 1 Schorch D-4138 Induction 315

Turbo 2 WED 355 AB2 Induction 450

Table 3 - Characteristics of the Turbo compressors

Although there is information regarding the nominal characteristics of these motors, they lack

proper documentation and there is little information about their behaviour under operating

y(x) = 0,027653x

0

20

40

60

80

100

120

140

160

0 1000 2000 3000 4000 5000 6000

Po

we

r co

nsu

mp

tio

n (

kW

)

Air Flow (m3/h)

Power(Air Flow)

13

conditions since they are older than the Aerzen compressors set. To overcome this problem

measurements during several weeks of operation were made with two power analysers

referenced as Fluke 1735 [4]. With these power measurement instruments it was possible to

record average power consumption in each interval of 15 minutes. Then, by matching the air

consumption per hour in each fermenter recorded manually by the operators with the power

registered by the Fluke analysers it was possible to sketch a characteristic curve of power

consumption (y) as a function of air volume (x) injected into the collector using a third order

polynomial regression, which was the one who best simulated the behaviour of the machines, as

it can be seen in figures 10 and 11.

Figure 10 - Power consumption as a function of air flow for T1

Figure 11 - Power consumption as a function of air flow for T2

y(x) = 8,29E-11x3 - 4,30E-06x2 + 6,40E-02x

0

50

100

150

200

250

300

350

0 2000 4000 6000 8000 10000 12000 14000

Po

wer

co

nsu

mp

tio

n (

kW)

Air Flow (m3/h)

T1 - Power(Air Flow)

y(x) = 2E-10x3 - 7E-06x2 + 0,0835x

0

50

100

150

200

250

300

350

400

450

500

10500 11000 11500 12000 12500 13000 13500 14000 14500 15000

Po

wer

co

nsu

mp

tio

n (

kW)

Air Flow (m3/h)

T2 - Power(Air Flow)

14

The data used for the previous figures can be consulted in Appendix B. These data was obtained

from the measurements when only Turbo 1 or Turbo 2 were working alone, because when they

are working simultaneously the air injected into the collector comes from both and it is impossible

to assess exactly how much air each Turbo is pumping. Thereby, the data acquired in the

moments where only one Turbo was working is assuredly more precise. However, although it is

hard to know how much air each Turbo compressor pumps when both are working at the same

time, their way of operating is not random: when both are turned on, T2 is almost at maximum

power while T1 pumps the remaining needed air into the collector. It will be seen in chapter 5 that

T1 is on when required air flow is between 0 to 10500 m3/h, T2 is on from 10500 to 15000 m3/h

and T1 and T2 are both turned on when the air flow is over 15000 m3/h. Obviously there are

fluctuations in this borders and that is the reason why data was obtained in the periods of time

when only either T1 or T2 were pumping air into the collector alone, for a more precise modelling.

Figure 12 - Turbo 1

Figure 13 - Turbo 2

2.3.3 Holmes compressors

There are two Holmes compressors, H1 and H2, which mainly feed F1 and F2 only for air

circulation purposes, respectively. Under rare circumstances such as F3, F4 and F5 being without

any fermentation going on, H1 and H2 will be responsible for pumping air into the collector to

assure air circulation and avoid bacteria and impurities entrance.

These compressors have motors from Brook Crompton with nominal power of 22 kW. Since their

power is much lower than the main compressors and approximately feed always the same air

quantity (1000 m3/h), they will have small impact in the optimization algorithm, as it will be seen

in chapter 7. So it was assumed that they always consume the nominal power of 22 kW as a

simple way to incorporate them in the simulation program.

15

Figure 14 - Holmes 1 and Holmes 2

2.3.4 Separators

There is a set of three separators Westfalia HDA75 with an induction motor of 37kW each.

Depending of what kind of yeast is going to be produced, one or three separators are going to be

used. If it is cream or pressed yeast, the three separators will be used. If it is dry yeast only one

separator will be used because later it will be transferred to another facility intended only to the

drying process, which is outside the scope of this thesis. So it was important to ascertain if the

power consumption of the separators is significant or not. Again, like with T1 and T2, there are

not proper documentation regarding these separators. After weeks of registering daily energy

consumption given by an energy meter linked only to the separators, it was verified that their

consumption is very small comparing to the consumption of the main compressors. Therefore,

the separators were kept out of the program as a source of energy consumption.

Figure 15 - Separators

16

3 Portuguese Tariff

System

17

3.1 Overview

The main goal of the activities of the National Electric System (SEN) is to deliver electric energy

adequate to the needs of the consumers, either quantitatively or qualitatively, taking into account

rationality and efficiency principles regarding the used means in all its activities from the electric

energy production to the supply of the final consumer. Electric energy is an essential good and

as such must fulfil specific requirements, among which stand out the security, regularity and

quality of its provision, guarantee of universality of the service, guarantee of connection to the

grid to all the customers and client protection concerning tariffs and prices. This sector is divided

in four activities: production, transmission, distribution and commercialization. Commercialization

has been an activity associated to distributors, but since the market liberalisation these two

activities are treated separately. With this liberalisation every consumer has the right to choose

its own electric energy retailer, so it will be expected an increase in the competition between

retailers, which will be reflected on the electric energy prices and on an improvement of quality

service, which in turn will elevate the satisfaction of the consumers [5].

The access tariffs and the way they are calculated is defined in the Tariff Regulation of the

Regulation Entity of the Energy Services (ERSE) [B]. This regulation must promote fair tariffs

concerning resources utilisation, economic and financial balance of the regulated companies,

quality of electric energy supplying and stability of tariff evolution. Therefore, the access tariffs

should be determined in an additive way, i.e. each client must pay the costs they cause on each

activity of the energy sector, which will have different tariffs accordingly. Figure 12 exhibits the

access tariffs for the liberalised market [5].

Figure 16 - Access Tariffs for the liberalised market – adapted from [5]

18

As it can be seen in Figure 12, in the liberalised market there are regulated costs paid by all

consumers defined by ERSE concerning network access. Non-regulated energy and retail prices

are negotiated between the selling company and the consumer. Case the consumer is not

inserted yet in the liberalised market, energy and retail prices are therefore fixed by a transient

tariff regulated by ERSE, whose price is higher than the prices practiced in the liberalised market.

This is an incentive for the consumer to adhere to the liberalised market and make an informed

choice of what is the best company to buy energy from [5].

These regulated and non-regulated prices from the access tariffs also vary accordingly to the so-

called “hourly periods”. Hourly periods are differentiated in daily cycle (hourly periods remain the

same during all week) and weekly cycle (hourly periods on Saturday and Sunday are different

from other week days). Each hourly period can be divided into super peak, peak, off-peak and

super off-peak hours. Depending on the type of consumer, i.e. the voltage regime used by the

consumer - extra high voltage, high voltage, medium voltage, low voltage normal or low voltage

special - there may only be a distinction between peak and off-peak hours (bi-hourly) or between

super peak, peak and off-peak hours (tri-hourly), as well as there may only be a certain cycle

available to choose [5].

3.2 Lallemand Contracted Tariff

Lallemand is connected to the medium voltage grid. From ERSE regulations, there are only two

options available to this company: the weekly cycle and the optional weekly cycle, both having 4

hourly periods (super peak, peak, off-peak and super off-peak). At this moment, the company has

contracted the weekly cycle and its retailer is Iberdrola.

For the medium voltage consumers, such as Lallemand, the electric energy invoice discriminates

several costs associated to the activities costs pictured in figure 12, and some of them vary

according to the time periods when the energy is consumed. The electric invoice contemplates:

Active energy invoiced (€/kWh)

Active energy consumed in each time period of the contracted tariff. Its cost is

negotiated between the company and its retailer

Energy network access term (€/kWh)

This term is relative to the usage of transmission and distribution power lines and

also varies according to the hourly periods. Its cost is regulated and fixed by

ERSE, so it is independent from the retailer

19

Power network term

o Contracted power (€/kWday)

Maximum average power registered in any uninterrupted interval of 15

minutes over the last 12 months, including the one concerning the invoice

o Power consumed in peak hours (€/kWday)

Total energy consumed in peak hours, divided by the number of peak

hours existent in the period relative to the invoice

Reactive energy term (€/kVArh)

Total reactive energy consumed

Special tax over electricity consumption (€/kWh)

The weekly cycle and optional weekly cycle hourly periods are depicted in table 3 and table 4.

Weekly cycle for Continental Portugal

Winter time Summer time

Monday to Friday Monday to Friday

Super Peak 09:30 - 12:00

18:30 – 21:00 Super Peak 09:15 – 12:15

Peak

07:00 – 09:30

12:00 – 18:30

21:00 – 24:00

Peak 07:00 – 09:15

12:15 – 24:00

Super Off-Peak 02:00 – 06:00 Super Off-Peak 02:00 – 06:00

Off-Peak 00:00 – 02:00

06:00 - 07:00 Off-Peak

00:00 – 02:00

06:00 – 07:00

Saturday Saturday

Peak 09:30 – 13:00

18:30 – 22:00 Peak

09:00 – 14:00

20:00 – 22:00


Off-Peak

00:00 – 02:00

06:00 – 09:30

13:00 – 18:30

22:00 – 24:00

Off-Peak

00:00 – 02:00

06:00 – 09:00

14:00 – 20:00

22:00 – 24:00

Sunday Sunday


Off-Peak 00:00 – 02:00

06:00 – 24:00 Off-Peak

00:00 – 02:00

06:00 – 24:00

Table 4 - Weekly cycle hourly periods

20

Optional Weekly cycle for Continental Portugal

Winter time Summer time

Monday to Friday Monday to Friday

Super Peak 17:00 – 22:00 Super Peak 14:00 – 17:00

Peak

00:00 – 00:30

07:30 – 17:00

22:00 – 24:00

Peak

00:00 – 00:30

07:30 – 14:00

17:00 – 24:00


Off-Peak 00:30 – 02:00

06:00 - 07:30 Off-Peak

00:30 – 02:00

06:00 – 07:30

Saturday Saturday

Peak 10:30 – 12:30

17:30 – 22:30 Peak

10:00 – 13:30

19:30 – 23:00


Off-Peak

00:00 – 03:00

07:00 – 10:30

12:30 – 17:30

22:30 – 24:00

Off-Peak

00:00 – 03:00

07:30 – 10:00

13:30 – 19:30

23:00 – 24:00

Sunday Sunday


Off-Peak 00:00 – 04:00

08:00 – 24:00 Off-Peak

00:00 – 02:00

08:00 – 24:00

Table 5 - Optional weekly cycle hourly periods

21

4 Problem Identification

22

To make an appropriate modelling of the whole problem, it is necessary to define correctly the

problem at first. Only by doing this, it will be possible to define the proper decision variables,

identify the existent constraints, and finally create the objective function to be optimized by the

optimization algorithm within the simulation program [6].

The majority of expenses paid by Lallemand comes from electric energy consumption. Thus it

was important to study and analyse all sources of energy consumption and look for inefficient

practices in order to solve them. The great consumers in this company can be divided as follows:

Evaporator

Fermentation process

o Air pumping

o Water pumping for cooling

o Pumping for yeast circulation

o Separation

Drying facility

This thesis focus only in the fermentation process, namely in the air pumping as the energy

consumer, which is in fact the activity where most inefficiencies occur. The main goal is trying to

solve one big problem of the fermentation process: weekly plans done by the production manager

don’t take into account the hourly periods present in the contracted tariff. Therefore, consumption

peaks often occur in the super peak hours, leading to an aggravation in the costs by the end of

each month. This can be treated as a scheduling problem, aiming towards the optimization of

electric energy consumption costs.

The simulation program will also allow to evaluate which tariff is the best one to be contracted,

since the company has not done any investigation regarding this aspect in many years.

However, other problem arises in what concerns the company as a whole. Contracted power is

often exceeded and, as previously explained, the company will have to pay this new higher value

for the next 12 months. Usually it happens after the factory has some maintenance interruption

for several hours, or when some fermenters or other energy consumers have to be stopped for

some reason. Why? Because, as soon as the maintenance/problem is over, everything is turned

back on right away. So all machines start up more or less at the same time and the different

processes are running parallel. Therefore the combined power is enough to exceed the contracted

power. The fermentation process itself is not enough to achieve the company’s usual values of

contracted power, but, together with the evaporator - which is a huge consumer - the drying

facility, the water pumping and also with other smaller consumers, such as lighting and

refrigeration, it can easily climb over to higher values. Given that this situation is not contemplated

in the program, the solution comes by creating awareness to all workers and managers for this

23

problem. After a maintenance break, instead of turning everything back on immediately, operators

must allow an interval between the beginning of each process, which is completely feasible since

a deviation of 2 or 3 hours does not affect at all the production of the company.

Finally, the last problem detected is the stoppage of production due to breakdown of equipment,

lack of feedstock or human mistakes. Hence, this problem is not predictable and such as with the

contracted power problem, the solution passes through raising awareness to all working

personnel. It is very common for a weekly plan to be changed during the course of the week in

consequence of these sudden problems. As it will be seen later, in chapter 7.3, this fact reduces

the efficacy of the obtained optimized plans because the program does not comprise such

stoppages and plan alterations.

24

5 Mathematical

Formulation of the

Problem

25

5.1 Decision Variables

In the production process there are 5 different fermenters, which can operate in parallel. Each

fermentation consists in a cycle with variable duration, divisible in three distinct tasks: initialization,

fermentation and separation. Taking into account only the time constraint of one week (168

hours), it will be considered that fermenters F2, F3 and F5 can have a maximum of 8

fermentations, F1 a maximum of 7 fermentations and F4 a maximum of 5 fermentations,

according to table 1. Given that fermentations are initialized manually by an operator, for

practicability matters of the production plans, fermentations can only be initialized every 30

minutes. Consequently it will be considered for the optimization mathematical model that the time

variable is a discrete variable with intervals of 30 minutes. Then, time can assume integer values

from 1 to 336 (168 hours is equal to 336 half-hours).

The first step in creating the optimization mathematical model is the definition of the decision

variables. Decision variables represent quantifiable decision that can be made in a certain

problem [6]. For this particular scheduling problem, to each task (fermentation cycle) were

associated two decision variables. The first decision variable is a binary one: 1 means the task is

scheduled, 0 means it is not scheduled. The second variable is an integer one, which identifies

the time interval since the end of the last fermentation in a given fermenter until the beginning of

the next one. Mathematically, this set of variables for this optimization problem can be defined as

follows:

Being N the maximum number of tasks (fermentations) that can occur, for each task 𝑖 are defined

two variables 𝑥𝑖 and 𝑥𝑖+𝑁 with 𝑖 ∈ [1,𝑁]:

𝑥𝑖 – Integer variable

𝑥𝑖+𝑁 – Binary variable

For the present optimization problem, 36 fermentations can happen in one week, so 𝑁 = 36,

totalising 72 variables. In table 5 is shown the association between these variables and the

fermentations in each fermenter.

Fermenter Integer variables Binary variables

F1 x1 to x7 x37 to x43

F2 x8 to x15 x44 to x51

F3 x16 to x23 x52 to x59

F5 x24 to x31 x60 to x67

F4 x32 to x36 x68 to x72

Table 6 - Integer and binary variables for each fermenter

26

5.2 Energy Consumption Modelling

The total energy consumption, in each interval of time t, is given by the sum of all the power

consumed in each machine considered for the optimization problem defined in chapter two. So it

is given by the sum of the following parcels:

𝐸𝑡𝑜𝑡𝑎𝑙(𝑡) = 2𝐸𝐴1(𝑡) + 2𝐸𝐴2(𝑡) + 𝐸𝑇1(𝑡) + 𝐸𝑇2(𝑡) + 𝐸𝐻1(𝑡) + 𝐸𝐻2(𝑡) (1)

𝐸𝑡𝑜𝑡𝑎𝑙 – Total energy consumption in each time interval

𝐸𝐴1 – Energy consumption in each Aerzen feeding F1 in each time interval

𝐸𝐴2 – Energy consumption in each Aerzen feeding F2 in each time interval

𝐸𝑇1 – Energy consumption by Turbo T1 in each time interval

𝐸𝑇2 – Energy consumption by Turbo T2 in each time interval

𝐸𝐻1 – Energy consumption by Holmes H1 in each time interval

𝐸𝐻2 – Energy consumption by Holmes H2 in each time interval

As it was explained in chapter 2.3.4, separators are not considered to the optimization problem,

given their low energy consumption compared to the main energy consumers at the process and

their complex behaviour.

5.2.1 Aerzen Compressors Energy Consumption

In chapter 2.2 was made a statistical analysis to get an average air consumption profile over the

time of one fermentation cycle for the Aerzen compressors, and in chapter 2.3.1 was obtained

the relation between power and air consumption. Now, it must be expressed in mathematical

terms these relations in order to insert the power consumption of the Aerzen compressors into

the program.

Air consumption is dependent of the state of the fermentation. Therefore, it is dependent of the

plan scheduling and, consequently, of the time. The function that relates the air consumption in

each time interval given a certain plan 𝑥 can be formulated generically:

𝑎𝑖𝑟𝐴𝑒𝑟𝑧𝑒𝑛[𝑡] = 𝐹𝑎𝑖𝑟𝐴𝑒𝑟𝑧𝑒𝑛(𝑥[𝑡]) (2)

𝑎𝑖𝑟𝐴𝑒𝑟𝑧𝑒𝑛 – Air consumed by each Aerzen compressor in each time interval

𝐹𝑎𝑖𝑟𝐴𝑒𝑟𝑧𝑒𝑛 – Air consumption given a scheduled plan in each time interval for each Aerzen

compressor

𝑥 – Scheduled weekly plan

27

𝑡 – Discrete time: 𝑡 ∈ [1: 336]

On the other hand, power as a function of air consumption, as it was already estimated in chapter

2.2, can be written as follows:

𝑃𝐴𝑒𝑟𝑧𝑒𝑛(𝑎𝑖𝑟𝑎𝑒𝑟𝑧𝑒𝑛[𝑡]) = 0.027653𝑎𝑖𝑟𝐴𝑒𝑟𝑧𝑒𝑛[𝑡] (3)

𝑃𝐴𝑒𝑟𝑧𝑒𝑛 – Power consumed by each Aerzen compressor as a function of pumped air volume

Hence the energy consumed in each interval of time for each Aerzen compressor is:

𝐸𝐴𝑒𝑟𝑧𝑒𝑛[𝑡] = 𝑃𝐴𝑒𝑟𝑧𝑒𝑛(𝑎𝑖𝑟𝐴𝑒𝑟𝑧𝑒𝑛[𝑡]) × Δ𝑡 (4)

∴ 𝐸𝐴𝑒𝑟𝑧𝑒𝑛[𝑡] = 0.027653𝐹𝑎𝑖𝑟𝐴𝑒𝑟𝑧𝑒𝑛(𝑥[𝑡]) × Δ𝑡 (5)

Δ𝑇 – Power integration constant: Δ𝑡 = 0.5h (30 minutes)

5.2.2 Turbo Compressors T1 and T2 Energy

Consumption

Energy consumption in T1 and T2 depends on the instantaneous air consumption in the collector.

In chapter 2.3 was estimated the average air consumption profiles for F3, F4 and F5, which are

the fermenters connected to the collector. Adopting the same approach used with the modelling

of Aerzen compressors consumption, it is again necessary to acquire a function that, given a

certain scheduled plan x, determines the respective air consumption during each time interval in

the collector and by each Turbo individually. Similarly, these functions are formulated in equation

6, equation 7 and equation 8:

𝑎𝑖𝑟𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟[𝑡] = 𝐹𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟(𝑥[𝑡]) (6)

𝑎𝑖𝑟𝑇1[𝑡] = 𝐹𝑎𝑖𝑟𝑇1(𝑥[𝑡]) (7)

𝑎𝑖𝑟𝑇2[𝑡] = 𝐹𝑎𝑖𝑟𝑇2(𝑥[𝑡]) (8)

𝑎𝑖𝑟𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟 – Air injected to the collector in each time interval

𝐹𝑎𝑖𝑟𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟 – Air injected into the collector given a scheduled plan in each time interval

𝑎𝑖𝑟𝑇1 – Air pumped by Turbo T1 in each time interval

𝐹𝑎𝑖𝑟𝑇1 – Air pumped by Turbo T1 given a scheduled plan in each time interval

𝑎𝑖𝑟𝑇2 – Air pumped by Turbo T2 in each time interval

28

𝐹𝑎𝑖𝑟𝑇2 – Air pumped by Turbo T2 given a scheduled plan in each time interval

From the total air consumption during each time interval in the collector, the associated energy

consumption is going to be calculated. Since each pair of Aerzen compressors feeds only one

fermenter, it is easy to know when they are operating: they are turned on if a fermentation is

occurring, or they are turned off if there is none. Now for T1 and T2 the situation is more

complicated. Since they both are connected to a common collector, the way they are turned on

and off depends on the air to be injected to the collector. Therefore, a way of operating depending

on the air consumption in the collector must be defined. Modelling the way of functioning of these

Turbo compressors has an added difficulty, due to the fact that the decision of turning them on

and off is made manually by the shift operators. However, shift operators comply with an

approximate mode of operation, which is summarized in table 7 and will be used in the program.

Aircollector[t] (m3/h) Turbo compressors

Aircollector <= 10500 T1 ON

T2 OFF

10500 < Aircollector <= 15000 T1 OFF

T2 ON

Aircollector > 15000 T1 ON

T2 ON

Table 7 – Approximate mode of turning on and off T1 and T2 depending on the air volume in the collector

When both Turbo compressors are on, it will be considered that T2 is at its maximum power (i.e.

it is injecting 15000 m3/h), while T1 is pumping the remaining air needed for the collector. After

defining for each quantity of air in the collector which of the machines were working (T1, T2 or T1

and T2), it will be determined the power consumed by each Turbo, using the curves that relate

power with air consumption estimated in chapter 2.2. These curves represent two functions

expressed in equation 9 and equation 10, for Turbo 1 and Turbo 2, respectively.

𝑃𝑇1(𝑎𝑖𝑟𝑇1[𝑡]) = 8,29 × 10−11𝑎𝑖𝑟𝑇1

3 [𝑡] − 4,30 × 10−6𝑎𝑖𝑟𝑇12 [𝑡] + 6,40

× 10−2𝑎𝑖𝑟𝑇1[𝑡], 𝑎𝑖𝑟𝑇1[𝑡] ≤ 10500 𝑚3/ℎ

(9)

𝑃𝑇2(𝑎𝑖𝑟𝑇2[𝑡]) = 2 × 10−10𝑎𝑖𝑟𝑇2

3 [𝑡] − 7 × 10−6𝑎𝑖𝑟𝑇22 [𝑡] + 0.0835𝑎𝑖𝑟𝑇2[𝑡],

10500 < 𝑎𝑖𝑟𝑇2[𝑡] ≤ 15000 𝑚3/ℎ

(10)

𝑃𝑇1 – Power consumed by Turbo T1 as a function of pumped air volume

𝑃𝑇2 – Power consumed by Turbo T2 as a function of pumped air volume

29

Now a binary function should be created in order to define if each Turbo is on or off.

Mathematically this function can be expressed generically in equation 11 and in equation 12 for

each Turbo:

𝑇1𝑠[𝑡] = 𝐹𝑇1(𝑎𝑖𝑟𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟[𝑡]) (11)

𝑇2𝑠[𝑡] = 𝐹𝑇2(𝑎𝑖𝑟𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟[𝑡]) (12)

T1s – Status of Turbo T1 in each time interval (on or off)






Hence the energy consumption of each turbo in each time interval is formulated in the next two

expressions:

𝐸𝑇1[𝑡] = [𝐹𝑇1(𝑎𝑖𝑟𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟[𝑡]) × 𝑃𝑇1(𝑎𝑖𝑟𝑇1[𝑡])] × Δ𝑇 (13)

𝐸𝑇2[𝑡] = [𝐹𝑇2(𝑎𝑖𝑟𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟[𝑡]) × 𝑃𝑇2(𝑎𝑖𝑟𝑇2[𝑡])] × Δ𝑇 (14)

The last two expressions can be re-written as a function of the scheduled plan x:

𝐸𝑇1[𝑡] = [𝐹𝑇1(𝐹𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟(𝑥[𝑡])) × 𝑃𝑇1(𝐹𝑎𝑖𝑟𝑇1(𝑥[𝑡]))] × Δ𝑇 (15)

𝐸𝑇2[𝑡] = [𝐹𝑇2(𝐹𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟(𝑥[𝑡])) × 𝑃𝑇2(𝐹𝑎𝑖𝑟𝑇2(𝑥[𝑡]))] × Δ𝑇 (16)

5.2.3 Holmes Compressors Energy Consumption

Each Holmes compressor works only when there is no fermentation stage going on F1 and F2,

respectively. For example, if F1 is in the initialization stage, separation stage or simply without

any process occurring, then H1 is turned on to assure air circulation. The same goes for F2 and

H2. Thus two binary functions can be generically defined to indicate the status of both fermenters

(1 means the fermenter has the fermentation stage in progress, 0 means otherwise).

𝐻1𝑠[𝑡] = 𝐹𝐹1(𝑥[𝑡]) (17)

𝐻2𝑠[𝑡] = 𝐹𝐹2(𝑥[𝑡]) (18)

30

𝐻1𝑠 – Status of H1 (on or off)



𝐻2𝑠 – Status of H2



As explained in chapter 2.3, Holmes consume a very small amount of energy compared to the

Aerzen or Turbo compressors. Therefore, it will be assumed they spend their nominal power every

time they are operating. Hence, the following expressions represent their energy consumption:

𝐸𝐻1[𝑡] = 𝐻1[𝑡] × 𝑃𝐻1 × Δ𝑇 (19)

𝐸𝐻2[𝑡] = 𝐻2[𝑡] × 𝑃𝐻2 × Δ𝑇 (20)

𝑃𝐻1 – Nominal power of H1 (22 kW)

𝑃𝐻2 – Nominal power of H2 (22 kW)

As it was previously done with the other compressors, the energy expressions can be re-written

as a function of the scheduled plan:

𝐸𝐻1[𝑡] = 𝐹𝐹1(𝑥[𝑡]) × 𝑃𝐻1 × Δ𝑇 (21)

𝐸𝐻2[𝑡] = 𝐹𝐹2(𝑥[𝑡]) × 𝑃𝐻2 × Δ𝑇 (22)

5.3 Energy costs modelling

In chapter 3 it was explained what is present in the monthly energy invoice. Accordingly, variables

for each term to be paid are going to be created in order to express, in the end, the sum of all

costs. Firstly, it should be defined four non-linear binary functions representing, respectively,

Super peak, peak, Super off-peak and off-peak hours depending on the contracted tariff and also

on the season (winter or summer hour).

{

𝐻𝑆𝑝[𝑡] = [0 1]

𝐻𝑝[𝑡] = [0 1]

𝐻𝑆𝑜𝑓𝑓[𝑡] = [0 1]

𝐻𝑜𝑓𝑓[𝑡] = [0 1]

(23)

31

𝐻𝑆𝑝 – Binary function indicating the time intervals corresponding to Super peak hours

𝐻𝑝 – Binary function indicating the time intervals corresponding to peak hours

𝐻𝑆𝑜𝑓𝑓 – Binary function indicating the time intervals corresponding to Super off-peak hours

𝐻𝑜𝑓𝑓 – Binary function indicating the time intervals corresponding to off-peak hours

Active energy invoiced

𝑎𝑐𝑡𝑖𝑣𝑒 𝑒𝑛𝑒𝑟𝑔𝑦 𝑐𝑜𝑠𝑡𝑠 →

{

𝑆𝑢𝑝𝑒𝑟 𝑝𝑒𝑎𝑘 ℎ𝑜𝑢𝑟 − 𝑐𝑆𝑝𝑎

𝑝𝑒𝑎𝑘 ℎ𝑜𝑢𝑟 − 𝑐𝑝𝑎

𝑆𝑢𝑝𝑒𝑟 𝑜𝑓𝑓 𝑝𝑒𝑎𝑘 ℎ𝑜𝑢𝑟 − 𝑐𝑆𝑜𝑓𝑓𝑎

𝑜𝑓𝑓 𝑝𝑒𝑎𝑘 ℎ𝑜𝑢𝑟 − 𝑐𝑜𝑓𝑓𝑎

(€/𝑘𝑊ℎ) (24)

Energy network access term

𝑒𝑛𝑒𝑟𝑔𝑦 𝑛𝑒𝑡𝑤𝑜𝑟𝑘 𝑎𝑐𝑐𝑒𝑠𝑠 𝑡𝑒𝑟𝑚 𝑐𝑜𝑠𝑡𝑠 →

{

𝑆𝑢𝑝𝑒𝑟 𝑝𝑒𝑎𝑘 ℎ𝑜𝑢𝑟 − 𝑐𝑆𝑝𝑛

𝑝𝑒𝑎𝑘 ℎ𝑜𝑢𝑟 − 𝑐𝑝𝑛

𝑆𝑢𝑝𝑒𝑟 𝑜𝑓𝑓 𝑝𝑒𝑎𝑘 ℎ𝑜𝑢𝑟 − 𝑐𝑆𝑜𝑓𝑓𝑛

𝑜𝑓𝑓 𝑝𝑒𝑎𝑘 ℎ𝑜𝑢𝑟 − 𝑐𝑜𝑓𝑓𝑛

(€/𝑘𝑊ℎ) (25)

Power network term

o Cost per kW of contracted power day - 𝑐𝑐𝑝 (€/𝑘𝑊𝑑𝑎𝑦)

Contracted power will not be considered in the program since its value remains almost the same

every month. When that value is exceeded, it is not only because of the fermentation process but

the sum of all the activities in the company.

o Consumed power in super peak hours cost - 𝑐𝑆𝑝𝐻 (€/𝑘𝑊𝑑𝑎𝑦)

To calculate the consumed power in super peak hours is necessary to establish a variable that

counts the number of super peak hours in one week. One must remember that the time variable

represents intervals of 30 minutes, therefore in the next expression one must multiply by this

integration constant, so the correct number of super peak hours is obtained.

𝑁𝑆𝑝𝐻 = ∑𝐻𝑆𝑝[𝑡]

336

𝑡=1

× Δ𝑇 (26)

𝑁𝑆𝑝𝐻 – Number of super peak hours in one week

32

Reactive energy term

This term is not going to be taken into account because Lallemand has a capacitor bank

connected to the grid. Therefore its value is very small or even zero sometimes.

Special tax over electricity consumption - 𝑐𝑡𝑎𝑥 (€/𝑘𝑊ℎ)

The energy consumption in each time period is now possible to represent:

𝐸𝑆𝑝𝐻(𝑥) = ∑𝐻𝑆𝑝[𝑡] × 𝐸𝑡𝑜𝑡𝑎𝑙[𝑡]

336

𝑡=1

(27)

𝐸𝑝𝐻(𝑥) = ∑𝐻𝑝[𝑡] × 𝐸𝑡𝑜𝑡𝑎𝑙[𝑡]

336

𝑡=1

(28)

𝐸𝑆𝑜𝑓𝑓𝐻(𝑥) = ∑𝐻𝑆𝑜𝑓𝑓[𝑡] × 𝐸𝑡𝑜𝑡𝑎𝑙[𝑡]

336

𝑡=1

(28)

𝐸𝑜𝑓𝑓𝐻(𝑥) = ∑𝐻𝑜𝑓𝑓[𝑡] × 𝐸𝑡𝑜𝑡𝑎𝑙[𝑡]

336

𝑡=1

(29)

𝐸𝑆𝑝𝐻 – Energy consumed in Super peak hours

𝐸𝑝𝐻 – Energy consumed in peak hours

𝐸𝑆𝑜𝑓𝑓𝐻 – Energy consumed in Super off-peak hours

𝐸𝑜𝑓𝑓𝐻 – Energy consumed in off-peak hours

Having the total energy consumed in each time period and the respective associated costs, it is

possible to assess the energy consumption total cost for a given plan 𝑥.

𝐶(𝑥) = (𝑐𝑆𝑝

𝑎 + 𝑐𝑆𝑝𝑛 + 7 ×

1

𝑁𝑆𝑝𝐻𝑐𝑆𝑝𝐻) × 𝐸𝑆𝑝𝐻(𝑥) + (𝑐𝑝

𝑎 + 𝑐𝑝𝑛) × 𝐸𝑝𝐻(𝑥)

+ (𝑐𝑆𝑜𝑓𝑓𝑎 + 𝑐𝑆𝑜𝑓𝑓

𝑛 ) × 𝐸𝑆𝑜𝑓𝑓𝐻(𝑥) + (𝑐𝑜𝑓𝑓𝑎 + 𝑐𝑜𝑓𝑓

𝑛 ) × 𝐸𝑜𝑓𝑓𝐻(𝑥) + 𝑐𝑡𝑎𝑥

×∑𝐸𝑡𝑜𝑡𝑎𝑙[𝑡]

336

𝑡=1

(30)

33

𝐶 – Total electric energy consumption cost for a certain scheduled plan 𝑥

5.4 Objective Function

The objective function measures the performance of the problem as a function of the decision

variables defined in 5.1 [6]. As mentioned in the objectives in section 1.2, the objective function

is created in order to minimize the costs of electric energy consumption per ton of produced

product. Therefore, it can be defined:

𝐹𝑜𝑏𝑗𝑒𝑡𝑖𝑣𝑒(𝑥) =

𝐶(𝑥)

𝑌(𝑥)

(31)

𝑌 – Tons of yeast produced in a given scheduled plan 𝑥

The total amount of produced yeast is calculated using the values of table 1.

𝑌(𝑥) = 30 × 𝑁𝐹1(𝑥) + 24 × 𝑁𝐹2(𝑥) + 20.5 × (𝑁𝐹3(𝑥) + 𝑁𝐹4(𝑥) + 𝑁𝐹5(𝑥)) (32)

𝑁𝐹𝑘 – Number of fermentations in fermenter k, in one week, for a given plan

The optimization problem goal is the minimization of the objective function formulated above.

Hence, it comes:

𝑀𝐼𝑁 (𝐹𝑜𝑏𝑗𝑒𝑡𝑖𝑣𝑒(𝑥)) = 𝑀𝐼𝑁 (

𝐶(𝑥)

𝑌(𝑥))

(33)

5.5 Constraints

Any restrictions the values that those decision variables defined in 5.1 can take represent the

problem constraints [6]. A set of constraints is associated to the problem of energy costs

minimization that will delimit the space of solutions of that same problem between feasible and

non-feasible ones. In this particular optimization problem, constraints are allied to resources

limitation, quantity of yeast produced requirements and the time limit of one week (168 hours).

34

5.5.1 Resources Constraints

In the fermentation process, the limitations of existent resources correspond to the usage of the

fermenters and separators. With the chosen decision variables (time interval between

fermentations), there will not be solutions that superpose the utilization of fermenters. So the only

resources constraint is the utilization of the separators.

The considered structure for modelling the resources constraint presupposes the usage of two

resources profiles: availability and utilization. This methodology is illustrated in figure 17 and it

comprises time and yeast quantity requirements constraints [2].

Profile (a), depicted in figure 17, represents the availability of a certain resource over time. Profile

(b) represents the requirements of utilization of that same resource, i.e. the necessity of using

that resource over time. On the other hand, profile (c) represents the difference between the

available and needed quantity. As such, profile (c) results from subtracting profile (a) for profile

(b). The existence of negative segments, in red, shows that the plan is not feasible once the

resources needed are higher than the ones available.

Figure 17 - Resources profile: (a) availability, (b) utilization and (c) feasibility – adapted from [1]

35

This method can be applied to the only constraint related to resources of this particular

optimization problem, the separators. There is only one set of separators, therefore their

availability profile over time is unitary. From a given scheduled plan x, the utilization of the

separators is determined over the whole timespan of one week, creating the so-called “utilization

profile”. The difference between these two described profiles will state if a plan x is feasible or not

feasible in what concerns this resources constraint. Thus, since the availability of the separators

is unitary, only one separation can occur at a time. If there are two fermentation processes in two

different fermenters that require a separation, or just part of it, at the same time then the plan is

not feasible. Mathematically one can translate this constraint as a non-linear function representing

the difference between availability and utilization profiles for a plan x. Hence this function should

be always greater or equal than zero in order to assess the scheduled plan x as feasible.

𝑈𝑠𝑒𝑝(𝑥) ≥ 0 (34)

𝑈𝑠𝑒𝑝 – Difference between availability and utilization profiles for a plan 𝑥

5.5.2 Production needs constraint

Every week there is a pre-specified goal of production, which takes into account stock necessities

and the orders received from clients, therefore being a variable objective.

It is possible to split the produced yeast into two types: type A and type B. Type B yeast can be

only fermented in fermenter F4 while type A yeast is produced in the remaining fermenters.

Mathematically the condition aforementioned is formulated in equation X and equation X:

𝑌𝐴(𝑥) = [𝑥𝑖=37:67]. [𝑜𝑢𝑡[1:31]]𝑇≥ 𝐴 → 𝑌𝐴 − 𝐴 ≥ 0 (35)

𝑌𝐵(𝑥) = [𝑥𝑖=68:72]. [𝑜𝑢𝑡[32:36]]𝑇≥ 𝐵 → 𝑌𝐵 − 𝐵 ≥ 0 (36)

𝑌𝐵 – Quantity of type B yeast produced for a given plan

B – Quantity of type B yeast required

𝑜𝑢𝑡 – Output of each fermenter in each scheduled fermentation

𝑌𝐴 – Quantity of type A yeast produced for a given plan

A – Quantity of type A yeast required

36

5.5.3 Time constraint

The last constraint to be considered for this optimization problem is the time constraint. As already

mentioned, each plan is made by the production manager on a weekly basis. Therefore, the sum

of all fermentation times in each fermenter and the intervals between them cannot overtake the

weekly 168 hours. This condition can be expressed mathematically in the next equations, for each

fermenter:

{

∑(𝑇𝐹1 + 𝑥𝑖) × 𝑥𝑖+36 ≤ 168

7

𝑖=1

∑(𝑇𝐹2 + 𝑥𝑖) × 𝑥𝑖+36

15

𝑖=8

≤ 168

∑(𝑇𝐹3 + 𝑥𝑖) × 𝑥𝑖+36

23

𝑖=16

≤ 168

∑(𝑇𝐹5 + 𝑥𝑖) × 𝑥𝑖+36

31

𝑖=24

≤ 168

∑(𝑇𝐹4 + 𝑥𝑖) × 𝑥𝑖+36

36

𝑖=32

≤ 168

(37)

𝑇𝐹𝑘 – Fermentation time in fermenter k, according to table 1

37

6 Implementation of the

Genetic Algorithm

38

6.1 Genetic Algorithm

Genetic algorithms are randomized search heuristic algorithms based on the natural selection

process present in biological evolution used to find solutions in optimization problems [7]. Genetic

algorithms were introduced by John Holland in 1975 [8] and they apply the principle of “survival

of the fittest”. Instead of searching just one solution at a time, this type of algorithm works with a

population of individuals (solutions). Each individual is encoded and represented by certain

characteristics that define their genetic material, called chromosomes. Genes are part of

chromosomes that represent a variable characterizing part of the solution. Moving from one

population of chromosomes to another happens with the so-called “natural selection”, where on

average the fitter chromosomes generate more offspring than the less fit ones. How does this

occur? The population is updated iteratively, where each iteration is called generation, and in

each generation genetic material exchange will happen between individuals through genetic

processes based on real ones such as crossover and mutation. Multiple solutions are evaluated

in parallel and the fittest individuals will be selected to breed a new generation through specific

selection process. Sometimes the best individuals can come across one generation to another

unaltered. This process is denominated elitism. The fitness of the solutions is evaluated

accordingly to a fitness function developed for the respective optimization problem. When the

stopping criteria is met, for example number of generations or the goodness of solution, the

search is finished. For very complex problems the optimal solution is very hard to achieve,

however a good solution is still important to obtain [3][9][10].

Complex problems with constraints and a wide range of solutions are difficult or even impossible

to represent using conventional math programming techniques [2]. For such problems, a method

that is based on parallel search for solutions and a smart way of creating and picking the best

ones, typical of evolutionary algorithms, is more suitable [9]. Genetic algorithms search efficiently

in large spaces and are robust in view of the complexity of the search problem [3]. Therefore,

given the complexity of the problem of this thesis due to the large space of solutions and a set of

constraints that must be simultaneously fulfilled, a genetic algorithm will prove to be an efficient

method of finding feasible solutions in a reasonable interval of time, not to mention it keeps the

whole modelling process very straightforward.

39

Figure 18 - Genetic algorithm basic cycle – adapted from [3]

6.2 Matlab Global Optimization Toolbox – Genetic Algorithm

The genetic algorithm applied to the current optimization problem of this thesis will be the

one present in Matlab Global Optimization Toolbox. Since this problem is coded with integer

variables and constraints, a mixed integer optimization will be required from Matlab. In fact, this

toolbox provides the regular genetic algorithm with an option to work solely with integer variables.

However, since it was not applied any alterations to this Toolbox, this integer genetic algorithm

solver presents some restrictions concerning its parameters and problems it can solve when

working with integer variables and constraints:

No linear or non-linear equality constraints. In each respective field should be

placed “[ ]”;

It is not possible to customize mutation, crossover and population creation

functions

Selection function is set to binary tournament only

No hybrid functions

To obtain integer variables, genetic algorithm uses special functions of mutation, crossover and

population creation [7].

40

It should also be noted that instead of a fitness function, this integer genetic algorithm uses a

penalty function. This penalty function includes a term for infeasibility, which will sum to the fitness

function due to constraints violations. If an individual represents a feasible solution, then the

penalty function is in fact the fitness function [11].

6.3 Parameters of Genetic Algorithm

As already seen in sub-chapter 6.2, Matlab Global Optimization Toolbox provides a genetic

algorithm that is suitable for problems with integer variables and constraints with some restrictions

to some functions. However, it is still possible to tune some parameters of some important

functions, such as crossover, mutation, selection and elitism. Next those functions will be

explained in a general manner and then the tuneable parameters relative to this algorithm will be

presented.

6.3.1 Selection

Selection is the process where parents are chosen to generate offspring for the next generation

through crossover and mutation. The point of selection is to choose fitter individuals hoping that

they will breed new individuals even with higher fitness [9]. Thus, to each individual is assessed

its fitness value and the way selection occurs depends on the selection implementation method:

stochastic uniform, roulette-wheel or tournament selection are just some examples.

The integer genetic algorithm uses the tournament selection. Each parent is chosen by randomly

picking Tournament Size players and then choosing the fittest individual between the contestants.

The winner of each tournament is selected for crossover and mutation to generate offspring.

Tournament Size is customizable and its value must be at least 2 (2 players per tournament). The

choice between contestants is made in a deterministic way: the fittest individual always beat the

less fit individual.

6.3.2 Elitism

Carrying over the best individuals from one generation to another is called elitism. These

individuals can be lost if by any chance they are not selected for reproducing or are altered by

crossover and mutation. Maintaining the best individuals causes the algorithm to converge more

quickly [2] and it has been proven by several researchers that elitism greatly improves the

performance of genetic algorithm [9].

41

For the integer genetic algorithm used in Matlab it is possible to customize the elitism property

adapted to integer problems (Elite Count) by choosing the number of best individuals that pass

from generation to generation unaltered.

6.3.3 Crossover

Crossover is a genetic operator responsible for exchanging genes between chromosomes, i.e.

exchange data between parents to form a crossover child. Crossover searches the solution

space, therefore enabling local search (exploitation) [3]. Crossover allows genetic variation and

innovation in a population [9].

The integer genetic algorithm uses a non-customizable special crossover function. Still it is

possible to customize the fraction of individuals subject to crossover (Crossover Fraction).

Crossover Fraction of 1 means all children are resultant from crossover between parents and

Crossover Fraction of 0 means all children are mutated ones, apart from elite children.

6.3.4 Mutation

Mutation is another genetic operator and it is responsible for randomly changing genes in

chromosomes, i.e. for randomly changing data in a parent to originate a mutated child. Since

mutation can create new solutions non-related genetically to their parents (contrary to crossover),

its solutions searching is considered to be global (exploration). Due to this global searching nature

of mutation, it ensures that the population does not get stuck in a permanent local solution [9].

Mutation function in the integer genetic algorithm is a special function, non-customizable. The

only way of customizing it is indirectly by changing the Crossover Fraction, as it was explained

above. Let’s imagine that there is a population of 100 individuals. If Crossover Fraction is 0.8, and

there are 5 elite individuals, then the offspring will be 95*0.8 = 76 crossover children and the

remaining 19 will be mutated children.

42

6.4 Implementation of the Genetic Algorithm to the

Optimization Problem

6.4.1 Encoding and Decoding

As it has been already seen in previous chapters, a genetic algorithm is constituted by individuals,

which by analogy with biologic terms can be denominated chromosomes. Chromosomes should

be the encoded representation of solutions for a problem, and they must be decoded in order to

evaluate their fitness. This process of encoding is crucial to the success of genetic algorithm [3].

The encoded process has already been made under the name of “decision variables”, as it is

shown in chapter 5.1. There are 72 variables: 36 are integer and 36 are binary. Each one of those

variables represent a gene. The group of all 72 variables represent a chromosome. The collection

of all pair of genes (xi, xi+36), each stating if a fermentation is or not scheduled and the respective

time interval passed since the last fermentation, characterizes the solution. Therefore there is an

integer encoding represented by a string of 72 integer variables. Its decoding is made by running

the simulation program that contains all the information about power consumption by the different

sources and energy prices in each time interval (modelling effectuated in chapter 5) with the given

solution, thus obtaining the fitness value of that solution. One should remember that the whole

purpose of this thesis is to minimize the energy costs per ton of yeast produced using a genetic

algorithm. This is the fitness function no less, as it was formulated in equation 31, used to assess

how fit an individual is.

6.4.2 Parameters Values of the Genetic Algorithm

It was explained in chapters 6.2 and 6.3 the integer genetic algorithm provided by Matlab Global

Optimization Toolbox and some of its customizable parameters. Now it is time to customize these

parameters and a few more taking into account the optimization problem of this thesis. In this

chapter it will be talked only about parameters that will be fixed and will not be subject of

alterations never again. In appendix C all parameters that can be altered by the user will be

explained along with the GUI.

Population size, crossover fraction, elite count and tournament size are the parameters to be

adjusted. All of these parameters are correlated in a non-linear way, and their arrangement

interferes greatly with the performance of the program. A suitable configuration for this

optimization problem may be completely misadjusted for a different problem. The average

performance of a population of individuals is expected to decrease generation after generation

[11]. However one does not want the convergence to be too fast, otherwise one might be stuck

in a local optimum since there are not enough variety between individuals of a population. On the

43

other hand, one does not want the convergence to be too slow, otherwise the program may never

find solutions since the individuals are too different genetically to form useful offspring. In

conclusion, it is needed to find a good balance between exploitation and exploration [2]. Given

the complexity of this particular optimization problem, the user will always be required to insert a

feasible initial solution, typically done by the production manager, or there might be the problem

of the program never finding any feasible solution at all. Therefore one should aim to invest more

in exploitation rather than in exploration because the weekly plans are usually close to their full

capacity, not leaving too much margin for big alterations.

The binary tournament is deterministic, which puts maximum selective pressure by selecting

always the best individuals for mating. Consequently, it contributes already a lot to the exploitation

of the solutions space. Therefore, the population size is expected to be significant in order to bring

diversity of solutions and explore more globally the searching space. Mutation also contributes to

exploration, which is inversely related to the crossover fraction. Finally, there is the tournament

size: the bigger it is, the more exploitation of the solutions space will happen. To find a good

balance between these parameters, several tests were made in the program, which contains the

whole modelled process and the genetic algorithm, and are presented in table 8, table 9 and table

10.

In each test, the program was run 10 times for each configuration and it was registered the worst

solution, the best solution and the average of all solutions of those 10 runs. The program had

already inserted a feasible initial population. Deviation for each configuration was made in relation

to the best solution and best average of all configurations. It was calculated using not the absolute

values of fitness of each compared solution but the difference of fitness between each compared

solution and the fitness of the initial population. During the tests it was observed that the program

would stagnate before 500 generations, reason why a limit of 500 generations was chosen as a

stoppage criterion.

44

Test 1: Weekly plan with a typical average goal of production – YB = 82ton; YA = 602.5ton;

Fitness value C(x) = 20.1488 €/ton

# Pop.

Size

Crossover

Fraction

Elite

Count

Tourn.

Size

Worst

(€/ton)

Average

(€/ton)

Best

(€/ton)

Deviation (%)

Average Best

1 50 0,8 5 2 19,7456 19,6972 19,6600 7,83 8,29

2 100 0,8 5 2 20,1488 20,0624 19,9088 82,36 54,97

3 50 0,8 5 3 20,1216 20,0945 20,0711 88,92 85,42

4 100 0,8 5 3 19,7355 19,7165 19,7022 11,77 16,21

5 200 0,8 5 3 19,8846 19,8013 19,7297 29,08 21,37

6 50 0,8 15 2 20,0229 19,9522 19,8257 59,88 39,38

7 100 0,8 15 2 19,7111 19,6852 19,6462 5,38 5,70

8 200 0,8 15 3 19,7610 19,6936 19,6643 7,08 9,10

9 200 0,8 15 2 19,7074 19,6683 19,6450 1,91 5,48

10 50 0,7 5 2 19,9492 19,7832 19,6416 25,37 4,84

11 100 0,7 5 2 20,1488 20,0725 20,0052 84,43 73,06

12 100 0,7 15 2 19,6655 19,6589 19,6158 - -

13 200 0,7 15 2 19,7843 19,7024 19,6570 8,88 7,73

Table 8 - Performance of the optimization algorithm for several parameters combinations for test 1

In green it is presented the most suitable configurations for this typical plan. Therefore, for the

following tests only these 5 configurations will be tested. If the other ones already have a poor

performance in this typical scenario, then there is no point in using them for further tests. In red it

is indicated the best value of all configurations concerning the average of all 10 runs and the best

run. Deviation is calculated in relation to these values.

Test 2: Weekly plan with a high goal of production – YB = 102.5ton; YA = 644.5ton; Fitness

value C(x) = 21.1698 €/ton

# Pop.

Size

Crossover

Fraction

Elite

Count

Tourn.

Size

Worst

(€/ton)

Average

(€/ton)

Best

(€/ton)

Deviation (%)

Average Best

1 50 0,8 5 2 20,7109 20,3769 20,1114 9,19 8,22

7 100 0,8 15 2 20,5136 20,3471 20,0166 5,77 -

9 200 0,8 15 2 20,5830 20,5094 20,4055 24,37 33,72

12 100 0,7 15 2 20,5480 20,2966 20,0688 - 4,53

13 200 0,7 15 2 20,6121 20,3169 20,0380 2,32 1,86


45

Test 3: Weekly plan with a low goal of production – YB = 61.5ton; YA = 529ton; Fitness

value C(x) = 23.2065 €/ton

# Pop.

Size

Crossover

Fraction

Elite

Count

Tourn.

Size

Worst

(€/ton)

Average

(€/ton)

Best

(€/ton)

Deviation (%)

Average Best

1 50 0,8 5 2 22,5070 22,4352 22,3770 21,90 37,33

7 100 0,8 15 2 22,4584 22,4355 22,4081 21,93 39,68

9 200 0,8 15 2 22,4483 22,4252 22,3705 20,89 36,84

12 100 0,7 15 2 22,4718 22,4476 22,4254 23,15 40,99

13 200 0,7 15 2 22,3785 22,2189 21,8829 - -


Analysing the three tests there is not any configuration of parameters that could be easily chosen

immediately. However, configuration #13 will be the one used for the genetic algorithm because

in the first two tests its results are very close to the best ones obtained with other configurations

and in the last test it was by far the best configuration. In fact, the last test had a low production

goal and that has not been happening often, but as already explained test #13 performed well in

other situations. Therefore, to cover a wider range of possibilities, test #13 is the one selected.

The following table summarizes the parameters that will be implemented in the genetic algorithm

of Matlab Global Optimization Toolbox:

Population Size Crossover Fraction Elite Count Tournament Size

200 0.7 15 2

Table 11 - Selected values for the parameters of the genetic algorithm

46

7 Results

47

In the previous chapters it has been built the so-called simulation program. It is constituted by the

production process model, the energy tariffs and finally by the genetic algorithm. Disregarding the

genetic algorithm, using solely the production process model and the energy tariffs in the program,

it is possible to estimate the energy costs and energy consumption of the factory plan, for the

weekly cycle tariff (current contracted tariff) or for the optional weekly cycle. The factory plan is

the plan that would be implemented by the production manager in a regular week, like it always

has been, without optimizing it. To optimize this plan, then it will be necessary to use the genetic

algorithm. Recalling what was explained in 6.4.2, it is needed to insert an already feasible plan in

the initial population of the algorithm. That initial plan will be precisely that factory plan.

There were 6 test weeks chosen in June and July. All the relative results (cost per ton of yeast

produced and total energy consumption) are presented in comparison to the values of the factory

plan with the current tariff (weekly cycle) of the respective week represented in tables 13, 15, 17,

19, 21 and 23. Also it is defined in tables 12, 14, 16, 18, 20 and 22 a minimum starting hour for

the first fermentation in each fermenter in each week due to unfinished fermentations that are still

in progress from the previous week.

Week 1: from 9th of June until 15th of June

o Production goal – Type A yeast = 644.5 ton; Type B yeast = 102.5 ton

o Minimum time for the 1st fermentation to start:

Fermenter Minimum starting hour

F1 Mon 00:00

F2 Mon 10:30

F3 Mon 12:30

F4 Mon 05:30

F5 Mon 07:30

Table 12 - Minimum time for the 1st fermentation to start in each fermenter in week 1

Week 1 Price (€/ton) Energy (kWh)

Factory plan 20.2877 148 090

Table 13 - Factory plan with contracted weekly cycle in week 1

Week 2: from 16th of June until 22nd of June

o Production goal – Type A yeast = 624 ton; Type B yeast = 82 ton


48


F1 Mon 00:00

F2 Mon 07:30

F3 Mon 10:30

F4 Mon 03:30

F5 Mon 17:30



Factory plan 20.1571 143 200


Week 3: from 30th of June until 6th of July

o Production goal – Type A yeast = 641 ton; Type B yeast = 102.5 ton



F1 Mon 11:30

F2 Mon 15:30

F3 Mon 07:30

F4 Mon 00:00

F5 Mon 17:30



Factory plan 18.8577 142 770


Week 4: from 7th of July until 13th of July

o Production goal – Type A yeast = 620.5 ton; Type B yeast = 82 ton


49


F1 Mon 15:30

F2 Mon 19:30

F3 Mon 06:30

F4 Mon 00:00

F5 Mon 13:30



Factory plan 19.0021 139 700


Week 5: from 14th of July until 20th of July

o Production goal – Type A yeast = 665 ton; Type B yeast = 61.5 ton



F1 Mon 15:30

F2 Mon 09:30

F3 Mon 07:00

F4 Mon 22:30

F5 Mon 18:30



Factory plan 19.7584 144 410


Week 6: from 21st of July until 27th of July

o Production goal – Type A yeast = 685.5 ton; Type B yeast = 82 ton


50


F1 Mon 15:30

F2 Mon 05:30

F3 Mon 00:00

F4 Mon 00:00

F5 Mon 18:30



Factory plan 19.3019 148 480


In section 7.1 the factory plan will be compared with the optimized plan for the current contracted

tariff (weekly cycle) already characterized in the tables above. In section 7.2 the factory plan with

the current tariff will be compared with the factory plan and the optimized plan with the other tariff

(optional weekly cycle). Finally, in section 7.3 the optimized plan given by the program will be

compared to the real results measured in the company during test weeks. Note that, for the

optimized plans, the results presented here are the best ones obtained after running the program

several times.

7.1 Factory plan vs Optimized plan with weekly cycle

The results for the optimization of the factory plan with the weekly cycle are showed in tables 24

to 29. The variation column is relative to the factory plan in the respective week already shown in

the previous section, as already explained. The power consumption profiles for the factory plan

and for the optimized plan are going to be compared taken into account the hourly periods present

in one week in figures 19 to 24. In those figures, red corresponds to Super peak hours, yellow to

peak hours, blue to off-peak hours and green to Super off-peak hours. One should remember that

the timespan goes until 336 because the time variable intervals are equal to half-hours.

51

Week 1 Price (€/ton) Energy (kWh) Variation (%) Weekly

savings (€) Price Energy

Optimized plan 19.4528 146 480 -4.12 -1.09 623.67

Table 24 – Results of the optimized plan compared to the factory plan with weekly cycle in week 1

Figure 19 - Comparison of energy consumption between the factory plan and the optimized plan with weekly cycle in week 1



Optimized plan 19.8087 142 420 -1.73 -0.54 245.97

Table 25 - Results of the optimized plan compared to the factory plan with weekly cycle in week 2


52



Optimized plan 18.4582 142 100 -2.12 -0.47 297.03





Optimized plan 18.4189 137 670 -3.07 -1.45 409.70



53



Optimized plan 19.3172 143 070 -2.23 -0.93 320.53





Optimized plan 19.0333 148 440 -1.39 -0.03 206.15



54

From the previous results it can be stated, generally, that the more filled the plan is, i.e. the higher

the production goal is, the greater is the difficulty in decreasing the energy costs per ton of yeast

produced. However, for some situations that does not happen. For example, in week 1, which

has a goal production of 747 ton, there is a costs reduction of 4.12% in relation to the factory plan

while in week 2, which has a goal production of only 706 ton, there is only a decreasing of 1.73%

of energy costs of the factory plan. This implies that the easiness of how the program can reduce

the energy costs is not only dependent on the production goal, but also on the minimum starting

times and on how the fermentations are arranged in the factory plan (which is the initial plan

inserted into the initial population of the genetic algorithm).

Looking at the figures comparing the power consumption between factory and optimized plan, it

is clear in all weeks that the program shifts higher consumption intervals into non Super peak

hours (marked in red), leading to a decrease in the final energy costs since these hourly periods

are the more penalising ones. Peak energy consumption intervals usually happen in off-peak (in

blue) or Super off-peak hours (in green).

Regarding energy consumption, although it is not the objective of the program reducing energy

consumption, there is a very small decrease verified in each tested week by optimizing the factory

plan.

7.2 Results with the optional weekly cycle

The results for the factory plan with the optional weekly cycle are going to be shown next. They

will be compared to the factory plan results with the weekly cycle (already presented in the tables

of section 7). Also, for each week the factory plan with the optional weekly cycle is going to be

optimized and then it will be subjected to comparison with the factory plan with the current tariff

too. These results are shown in tables 30 to 35. Furthermore, Lallemand has access to its private

page in Iberdrola website where it can be consulted the energy consumption every 15 minutes in

any desired period of time. With that, it is going to be compared the energy consumption in the

whole company, not only in the fermentation process, from January to August between the weekly

cycle and the optional weekly cycle in order to assess if it is profitable to switch the contracted

tariff.

With the optional weekly cycle the number of hours of each hourly period in one week remains

the same, differing only its disposition over the week, as it can be checked in tables 4 and 5 in

section 3.2.

55



Factory plan w/ optional

weekly cycle 19.8001 148 090 -2.40 - 364.23

Optimized plan w/

optional weekly cycle 18.8464 146 980 -7.10 -0.75 1 076.65

Table 30 – Results of the factory and optimized plan with optional weekly cycle compared to the factory plan with weekly cycle in week 1




weekly cycle 19.3256 143 200 -4.13 - 587.04

Optimized plan w/

optional weekly cycle 18.6663 142 420 -7.40 -0.54 1 052.50





weekly cycle 18.7265 142 770 -0.70 - 97.55

Optimized plan w/

optional weekly cycle 17.9306 142 440 -4.92 -0.23 689.30





weekly cycle 18.8433 139 700 -0.84 - 111.56

Optimized plan w/



56




weekly cycle 19.5949 144 410 -0.83 - 118.78

Optimized plan w/






weekly cycle 18.8717 148 480 -2.23 - 330.18

Optimized plan w/



Looking at the tables above, one can assess that for the fermentation process the optional weekly

cycle is undoubtedly more suitable than the weekly cycle. Moreover, the proportion of costs

reduction in relation to the factory plan with the respective tariff is bigger in the optional weekly

cycle than in the weekly cycle. For example, in week 1, the optimized plan (table 24) reduced

0.8349 €/ton from the factory plan with the weekly cycle (table 13), while the optimized plan in

that same week but with the optional weekly cycle (table 30) was able to reduce 0.9537 €/ton

from the factory plan with that same optional weekly cycle (table 30). The same was true for the

other 5 tests. Therefore, the disposition of the hourly periods during one week in the optional

weekly cycle seems to be more adequate to the optimization algorithm in terms of finding better

solutions than the weekly cycle.

However, since the fermentation process is not the only responsible for the company expenses,

it is important to verify if globally the company profits by changing from weekly cycle to optional

weekly cycle. In its private page on Iberdrola website, it is possible to download the energy

consumption discriminated in intervals of 15 minutes during any period of time. So, since the

beginning of this year, all months are going to be analysed in terms of electricity costs with both

tariffs. Table 36 shows the results for each month, indicating how much it would be paid in the

monthly invoice having the tariff with the weekly cycle and having the tariff with the optional weekly

cycle. Note that the costs do not cover the reactive energy consumption and the contracted power

term because they are independent of the contracted cycle.

57

Month Electric energy costs (€)

Weekly cycle

Electric energy costs (€)

Optional weekly cycle

Difference

(€)

January 151 611 151 547 -64

February 153 652 154 157 +505

March 163 878 163 906 +28

April 158 090 158 161 +71

May 166 519 167 028 +509

June 177 224 176 741 -483

July 179 054 179 491 +437

August 155 140 155 165 +25

Table 36 - Electric energy costs in the first 8 months of 2014 for the two different tariff cycles: weekly cycle and optional weekly cycle

Table 36 is inconclusive whether changing in to the optional weekly cycle is advantageous for the

company. The difference between the two cycles is far inferior to 1% in all these months, which

is not very significant. Nonetheless, if one observes again tables 30 to 35 it can be stated that

optimising the factory plan with the optional weekly cycle, in comparison to that same plan, allows

savings up to 712.42€ per week in the best case, which happens in week 1. The worst case from

all the tested weeks occurs in week 6, still the savings reach 307.23€ per week. If one takes the

worst case and convert its savings to the extent of one whole month, then it will be saved

1351.81€. So if one takes also the worst month to have the optional weekly cycle contracted,

which was May with a loss of 509€, and assuming the optimized plan allowed cost savings around

1351.81€, then the profit would still be 846.81€. So would the company have some advantage in

changing tariffs? Would not the optimized plan for the weekly cycle have a better profit margin?

Faced with these questions, one should now analyse the savings acquired in optimizing the

factory plan with the weekly cycle present in tables 24 to 29. The best week in terms of costs

reduction happen in week 1, where savings reach 623.67€, which is still less than the worst case

if the company had changed to optional weekly tariff and had optimized the factory plan!

Therefore, it seems appropriate for the company to change the contracted tariff.

7.3 Simulated optimized plans vs Tested optimized plans

In all the 6 tested weeks, one tried to implement the optimized plans acquired in chapter 7.1.

However, only in week 2 the weekly optimized plan was completely fulfilled. In the other weeks

either the plan was not implemented at all due to last hour problems in the factory or the plan was

totally altered in the middle of the week, again due to unforeseeable factory problems. Hence, the

58

comparison between the expected results given by the simulation program and the real ones are

going to be presented next.

One should remember that it was considered 3 sources of power consumption: Turbo

compressors, Aerzen compressors and Holmes compressors. For the two Turbo compressors it

was directly measured and registered their power consumption with two power analysers over

that week. For the Aerzen compressors, one took the air volume consumed by fermenters F1 and

F2 registered manually by the shift operators in that week and then used the expression relating

power consumption and air volume obtained in section 2.3.1 to get the consequent energy spent

by the four Aerzen compressors. For the Holmes compressors, it was assumed they worked at a

constant power of 22 kW when F1 and/ or F2 were not having any fermentation. Therefore, only

the energy consumed by the Turbo compressors corresponds exactly to the reality, while power

consumption in Aerzen and Holmes compressors was estimated. Now the comparison between

the approximate real energy consumption and respective costs and the energy consumption and

costs given by the optimized plan for week 2 is presented in table 37.

Week 2 T1

(kWh)

T2

(kWh)

4 x

Aerzen

(kWh)

2 x

Holmes

(kWh)

Total

energy

(kWh)

Total cost

(€)

Test 26 861 46 801 96 923 2 123 172 708 16 149

Simulation 17 548 37 675 84 274 2 926 142 423 13 372

Dev. (%) -34.67 -19.50 -13.05 +37.82 -17.54 -17.20

Table 37 - Test and simulation results using the optimized plan in week 2: comparison and deviation

Analysing table 37, the optimized plan simulated in the program gives energy consumption values

and consequent costs below the real ones. However, the factory plan used to obtain the optimized

plan has also its power consumption and associated costs calculated in this same program,

meaning that the relative difference between factory and optimized plans is more important than

their energy consumption and costs absolute values, which in this case are undervalued. In other

words, the way air profiles in the fermenters evolve over time and the power consumption curve

grows as the pumped air also increases is more important than having higher or lesser values in

comparison to the real ones. Why? Looking into the distribution of the different hourly periods in

the contracted tariff, as depicted in figures 19 to 24, the program will try to shift higher

consumptions from peak or Super peak hours to off-peak and Super off-peak hours. Thus, it is

not critical if a peak occurs at 700 kW or at 500 kW, for example, as long as the adjacent power

consumptions are below that value. Being itself a peak, the program will always try to move it

away from peak or Super peak hours.

59

Nonetheless, it is true that there are some big deviations from the real values. For T1 and T2 the

decision of turning them on and off is manual, which makes the boundaries of table 7, in section

5.2.2, variable. Also, Turbo 1 power characteristic was made only when Turbo 1 was working by

the reasons explained in 2.3.2, therefore having very little information about power consumption

with small values of air volume, situation which can occur when both Turbo are working. For that

reason, the slope of the curve obtained in figure 10, for power consumption values under 4000

m3/h, may not be very adequate. Both reasons mentioned before can explain why the deviation

of energy consumed in T1 given by the program is -34.67%. Figure 38 and figure 39 depict the

difference between power consumption over the test week 2 given by the simulation program and

the real values measured directly from the T1 and T2, respectively, with the Fluke power

analysers, where the difference between both is significant.

Figure 25 - Power consumption in week 2: simulation results vs real results for T1

Figure 26 - Power consumption: simulation results vs real results for T2

If one overlaps both figures, the main differences rest in those areas where the simulation

program assumed one machine would be working but in reality it was another. Also, clearly it is

60

seen that T1 is under characterized in terms of power consumption for the reasons previously

stated. Albeit power consumed given by the program in T2 is a little bit below the real values,

globally it represents relatively well this compressor, since it is always near the maximum power.

The Aerzen compressors have the smallest deviation from all the machines involved in this test

(-13.05%). They are relatively new and have proper documentation. Yet, their power consumption

in this week was not measured directly from the Aerzen compressors, but it was indirectly

obtained through the hourly manual register of air fed into F1 and F2. Moreover, the air profile

used in the program is an average one, which obviously will always differ from fermentation to

fermentation.

As it can be assessed in table 37, Holmes compressors consume very little energy. Both for the

program and for the real test, it was considered they would work at their nominal power of 22 kW,

which is an approximation. Hence, the deviation is mostly due to the time when these

compressors are operating. Since there is a bigger consumption in the program than in the real

test, one can verify that the air profiles of F1 and F2 were longer in reality than their average

profiles built for the program, meaning that Holmes compressors would work less time in that

week and, on the other hand, Aerzen compressors would consume more energy -and that is

precisely verified in table 37.

Regarding the total electric energy cost over week 2 for the fermentation process, the deviation

comes as a direct consequence from all the causes mentioned before for each source of energy

consumption.

61

8 Conclusions and

prospective work

62

8.1 Conclusions

In this thesis it was studied and characterized the production process of Lallemand Iberia SA in

order to search for energy inefficiencies and come up with solutions. Namely, it was fully

characterized the fermentation process and an optimization approach was made to reduce its

costs per ton of yeast produced. To do so, first, the air consumption profiles for each fermenter

were statistically estimated and the power consumption characteristic of the machines

responsible for pumping air into those fermenters was obtained. Then, the whole process was

modelled, inserting in the program those air and power consumption characteristics of the

fermenters and machines, respectively, and the energy tariffs. The decision variables that directly

represent the weekly plan and inherent scheduling constraints were also defined. In the end, it

was created the genetic algorithm as a means to search for better plans, in terms of energy costs,

than the factory plan originally made by the production manager.

By testing and choosing the parameters of the genetic algorithm that would better suit this

particular problem, a good solution is almost always obtained immediately in the first run of the

program with the algorithm without spending too much time. However, the space of solution is

very big and the algorithm itself cannot even find a feasible solution if it starts without an initial

feasible solution inserted in the initial population. Therefore, the factory plan made by the

production manager should always be given to the program. Despite providing the program with

leverage to now find good solutions more easily, the fact that the starting point is the factory plan

will make the genetic algorithm return an optimized plan not very distinct from that initial factory

plan, especially if the plan is very full. This is good in what concerns the normal behaviour of the

company and the type of plans the shift operators are used to deal with. If the optimized plan is

somewhat similar to the factory plan, then each worker will already be familiar with it, facilitating

their usual work.

Theoretically, the optimization algorithm applied to the modelling program allows the company to

significantly reduce costs, if one considerers that there is no investment needed besides the

optimization program. Moreover, given that the production manager does not take into account

the variable hourly periods of the tariff over each day, any effort in trying to incorporate this factor

in the weekly plan will produce positive results. With the current contracted tariff (weekly cycle)

the factory plans of the 6 tested weeks were improved and in the best tested week (week 1)

savings could stretch to values of 623.67€ per week. If one takes that value as base, monthly the

savings would be approximately around 2745€, which by looking at the electric energy expenses

in the month on June (presented in table 36) represents a decrease in costs of about 1.55%. It

may not seem much, but again the cost of investment lies only in the optimization program.

Furthermore, it is visible in the power consumption comparison over one week between the

factory and the optimized plan that in Super peak hours (red areas) the power consumed in the

optimized plan is almost always under the power consumed by the factory plan in those hours.

63

This is the main reason why it is possible to decrease the weekly costs with electric energy, since

consumption in Super peak hours is very high-priced in comparison to other periods of time.

After confirming the usefulness of optimizing the factory plan for the current contracted tariff, one

other issue arose: would the electric costs of production of the factory plan be decreased if the

company changed to the electric tariff with the optional weekly cycle, and by further applying the

optimization algorithm? If so, would the company in its whole benefit from that tariff changing?

Results in section 7.2 evidently present that by only changing the contracted tariff to the optional

weekly cycle the factory plan for the fermentation process has already smaller electric expenses.

If one optimize it, then the savings will be even higher than with the optimization of the factory

plan with the weekly cycle. However, the sum of all the company electric energy consumers, not

only the fermentation process, does not clearly tell if a change in tariff is advantageous or not per

se. It can provide savings in one month as it can provide losses in another. Nonetheless, savings

obtained from changing to the optional weekly cycle and from optimizing the factory plan with

such tariff subtracted of the monthly losses (or added to the monthly savings) of the whole

company from that same tariff alteration are still higher than the ones resultant from the

optimization of the factory plan with the weekly cycle contracted. Therefore, it is advisable for the

company to change its contracted tariff and take advantage of the simulation program created in

this thesis.

Inherently connected to an electric energy costs reduction, it is a reduction in the energy

consumption of the factory, although very small.

Finally, it was tested, in practice, the optimized plan during week 2. Power consumption in T1 and

T2 was directly measured using the Fluke power analysers, while Aerzen compressors power

consumption was indirectly taken from the air consumption in F1 and F2 registered manually by

the shift operators. Power consumption was assumed constant in the Holmes compressors, and

each of them only worked when F1 or F2 were not having any fermentation occurring,

respectively. Results show that there is a significant deviation from real values to the ones

obtained in the simulated program regarding power consumption in each machine. Consequently,

the total cost of consuming electric energy given by the optimized plan also has a discrepancy in

relation to the real cost. The main causes for that are: air volume is registered manually by shift

operators, for each fermenter an average air profile was drawn, power consumption curve in T1

lack of measurements for low air injection, T1 and T2 switching mode is made manually and the

power consumed by the Holmes compressors was assumed constant. This, however, does not

invalidate the process modelling in the program and respective optimization because, more

important than the absolute values, is the relative difference between factory and optimized plan.

The difference between simulated and real values are as true to the optimized plan as to the

factory plan. Hence, albeit absolute values of power consumption given by the program vary from

the real ones, the way that consume progresses over time is the same to both plans and for that

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reason the program will be able to shift high power consumptions from Super peak hours to other

periods of time.

Regarding the problem of exceeding the contracted power, it is advised for all working personnel

to avoid putting several processes starting at the same time. With that in mind, turning on a certain

part of the factory with a delay of one or two hours later is perfectly feasible and acceptable and

this good practice will be reflected in the monthly invoice.

Only one practical test was made due to the fact that in all other weeks problems occurred that

forced unpredicted stoppages, thus changing the optimized plan that should be implemented.

Stoppages like this often happen, either due to equipment breakdown - about which very little can

be done, besides the common maintenance procedures - or due to lack of resources. Concerning

the latter, the respective responsible personnel should better coordinate the storage of resources

depending on their needs to avoid situations like this.

Overall, the study of the fermentation process and its translation into a program that could

optimize it, as well as the energy consumption analysis in the company as a whole, allowed to

identify and propose possible solutions to decrease the costs related to electric energy

consumption. The factory will certainly benefit from implementing these measures, moreover

when the cost of investment is solely related to the optimization program.

8.2 Prospective work

The work developed in this thesis present a starting point for several possible studies in order to

improve even more energy efficiency and costs reduction and more faithfully represent the

production system of Lallemand. The most important topics that could be taken in consideration

for future works are:

Creation of random air profiles in the program based in a probabilistic distribution for each

fermenter;

Characterization of Holmes compressors;

Incorporation of the separators and water and yeast pumping systems in the fermentation

process;

Modelling the fermentation process using a different set of decision variables;

Customization of crossover, mutation and selection functions of the genetic algorithm

provided by Matlab to better fit this specific problem.

65

References

1. European Commission. “The 2020 climate and energy package”.

http://ec.europa.eu/clima/policies/package/index_en.htm [20/08/2014].

2. M. B. Wall. “A Genetic Algorithm for Resource-Constrained Scheduling”, PhD Thesis,

Massachusetts Institute of Technology, June 1996.

3. J. M. Sousa. OSE, Class Lecture, “Derivative-free optimization” [PowerPoint slides].

Instituto Superior Técnico, 2014.

4. FLUKE. “FLUKE 1735 Power Logger Manual”.

http://assets.fluke.com/manuals/1735____umeng0100.pdf [10/04/2014]

5. ERSE. http://www.erse.pt [20/04/2014].

6. F. S. Hillier, G. J. Lieberman. “Introduction to Operations Research”. 7th edition, McGraw-

Hill, January 2000, pp. 7-27.

7. The MathWorks Inc. Global Optimization Toolbox.

http://www.mathworks.com/products/global-optimization [12/05/2014].

8. J. Holland. “Adaptation in Natural and Artificial Systems”. MIT Press, 1992.

9. M. Mitchell. “An Introduction to Genetic Algorithms”, 5th edition, A Bradford Book The MIT

Press, 1999.

10. M. L. Pinedo, “Scheduling – Theory, Algorithms and Systems”, 3rd Edition, Springer,

2008, pp. 385-387.

11. O. de Weck. OCW, Lecture Notes, “An introduction to genetic algorithms” [PowerPoint

slides]. Massachusetts Institute of Technology, 2010.

http://ec.europa.eu/clima/policies/package/index_en.htm

http://assets.fluke.com/manuals/1735____umeng0100.pdf

http://www.erse.pt/

http://www.mathworks.com/products/global-optimization

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Appendix A

Aerzen GM 90S characteristics catalogue

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Appendix B

Power measurements with the Fluke 1735 power

analyser

The next figures represent the data acquired with the Fluke power analysers to characterize the

power consumption of T1 and T2, as it was done in chapter 2.3.2.

Figure 27 - T1 power consumption from 24 to 29 of April

Figure 28 – T2 power consumption from 24 to 29 of April

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Appendix C

Structure of the simulation program

The simulation program contains the modelled fermentation process, the electric tariffs and the

genetic algorithm. Figure 29 depicts how the program is structured.

Figure 29 - Structure of the program

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GUI.m

Main function where the variables changed by the user in the interface are received. They are the

initial plan (factory plan), lower bounds for that plan (minimum time for each fermentation in each

fermenter), the production goal, in tons, of mother and commercial yeast, the contracted tariff and

the tariff prices. The interface is programmed in this function, and all the subsequent functions

are called from here.

converter.m

The user inputs a plan in the interface by choosing the day of the week and respective starting

hour for each fermenter, as well as the minimum starting time for the first fermentation.

Converter.m converts the format “day_of_the_week hh:mm” into an integer from 0 to 336. For

non-scheduled fermentations, a default value is assigned to recognize that.

Error checking (includes verify.m and constraints.m)

After converting the user input time format into a treatable one, errors are checked. An error

message appears and the program abort when: fermentations of the inserted plan are not put in

the correct order; the minimum fermentation time is not respected; the production goal is not met;

the user filled the blanks for the production goal or for the tariff prices with incorrect digits (for

example by inserting characters where should be only numbers); the timespan is exceeded; the

constraints are not fulfilled.

variables.m

It transforms the integer numbers representing the fermentation into the decision variables (36

integer and 36 binary variables) formulated in chapter 5.1, so the simulation program can use

them.

Genetic algorithm

Here the inserted initial plan will be optimized. During this process, several functions are called:

fitness_func.m

It calculates the cost of electric energy consumption per ton of yeast produced.

get_price.m

It calculates the total energy cost in one week for a given plan, taking into account the contracted

tariff.

get_power.m

It gives the power consumed by each of the considered compressors in the simulation program

in each time interval using the power characteristics acquired in chapter 2.

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get_air.m

It returns the air circulating in the collector (pumped by T1 and T2) and the air pumped by the

Aerzen compressors in each time interval.

startstop.m

It returns the starting and ending times of each fermentation in each fermenter.

get_out.m

It calculates the total yeast (mother and commercial) produced in a given plan.

constraints.m

The constraints should be matched for the plan to be considered feasible. Production goal should

be met, timespan should not be exceeded and only one separation can occur at a time.

get_sep.m

Returns the number of separations happening in each time interval. If it is bigger than 1, then the

constraints will not be fulfilled.

get_len.m

It calculates the time that all fermentations in each fermenter and intervals between them take. It

cannot exceed the timespan (336), otherwise constraints will not be met.

End of genetic algorithm

convert_back.m

After the optimization algorithm finishes (it reaches 500 generations), the optimized plan is

obtained. Since it is coded with decision variables, it will be converted back to a user friendly

format (“day_of_the_week hh:mm”).

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GUI

The interface for the program in this thesis was made in order to make it easy for the production

manager to create optimized plans. The production manager must always perform the factory

plan first, then insert it in the GUI as an initial plan, so the program can find feasible and better

solutions. The GUI can be seen in figure 30.

Figure 30 - GUI

Panels F1 to F5

Here the starting time for each fermentation must be selected. All fermentations must respect

constraints and they must be selected chronologically, from top to bottom. Otherwise an error

message will be presented. The minimum time of the first fermentation must also be selected. In

each panel, in the right column one chooses the day of the week and in the left column one

chooses the starting hour.

Panel “Produto (toneladas)”

The objective of production of the week must be inserted and must match the quantity possible

to obtain with the factory plan. Values are in tons. In the top blank must be inserted the quantity

of commercial yeast and in the top blank must filled with the quantity of mother yeast. Other

characters than digits will trigger an error message.

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Panel “Tarifa”

Whether the season is in the winter hour or in the summer hour, the option should be selected

accordingly in the top pop-up menu.

The tariff contracted by Lallemand should also be selected in the bottom pop-up menu.

Panel “Preços Tarifa”

Whenever prices are updated, they must be changed in the respective blanks.

“Nome do documentos a ser criado”

The name of the document to be created with the optimized plan should be written in that blank,

right next to the button “Optimizar” than runs the program.

After the program runs, a message box summarizing the result will appear (Figure 31), indicating

the cost per ton of yeast produced of the factory and optimized plans and the savings achieved

in that week. It will also mention that a document with the name wrote in the blank for that purpose

in the interface. The document summarizes the results too, and it will present the starting times

of each fermentation in this new optimized plan, as seen in figure 32, so the production manager

can easily draw it.

Figure 31 - Summarizing pop-up message

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Figure 32 - Document created with the new optimized plan and with the summary of the results

Documents

Optimization of the Production Process of Lallemand Ibéria ... · Supervisors: Prof. Paulo José da Costa Branco ... Then I thank Eng. Sandro Ratinho, ... 3 1.3 OBJECTIVES