Optimizing Water Tank Levels  

Using Genetic Algorithms  

 
Master’s thesis in Sustainable Energy Systems 

 

ALVAR WIKSTRÖM 

 

 

 

 

 

DEPARTMENT OF ARCHITECTURE AND CIVIL ENGINEERING 

CHALMERS UNIVERSITY OF TECHNOLOGY 

Gothenburg, Sweden 2025 

www.chalmers.se 



II 
 

 

MASTER’S THESIS 2025: ACEX30 

Master’s Thesis in Sustainable Energy Systems 

Supervisors: Behroz Haidarian and Glen Nivert  

Examiner: Thomas Pettersson 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Department of Architecture and Civil Engineering 

CHALMERS UNIVERSITY OF TECHNOLOGY 

Gothenburg, Sweden 2025 

 



III 
 

 

Optimizing Water Tank Levels Using Genetic Algorithms 

ALVAR WIKSTRÖM 

 

 © ALVAR WIKSTRÖM, 2025.  

 

 

Supervisor: Behroz Haidarian and Glen Nivert, Kretslopp och vatten, Göteborg stad  

Examiner: Thomas Pettersson, Chalmers University of Technology  

 

 

Degree project report 2025  

Department of Architecture and Civil Engineering 

Chalmers University of Technology  

SE-412 96 Gothenburg  

Sweden Telephone 

+46 31 772 1000 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 



IV 
 

Optimizing Water Tank Levels Using Genetic Algorithms 
ALVAR WIKSTRÖM  

Department of Architecture and Civil Engineering 
Chalmers University of Technology  

 

Abstract  

This thesis presents a practical optimization framework for energy-efficient pump scheduling in water 

distribution systems. It combines the practicality of rule-based control with the global-search power 

of genetic algorithms. A novel setpoint curve encoding scheme is introduced, in which daily tank-

level targets are parameterized by a small set of meaningful coefficients (baseline, peak/dip timing 

and amplitude, and curvature descriptors). These key parameters are then optimized using a custom 

genetic algorithm, coupled with EPANET-driven hydraulic simulations. Constraint handling is 

managed by penalty functions for demand security, hydraulic feasibility, reservoir volume balance 

and pump maintenance. The framework is first demonstrated on the simplified NET-1 hydraulic 

network, providing insight on how to algorithm operate. The optimization algorithm is subsequently 

applied to a calibrated high-pressure zone (HPZ-G) of the Gothenburg water network, using historical 

operational data for model validation. Results indicate that the optimized setpoint curves can reduce 

energy cost, whilst still hydraulic and operational constraints. However, certain data gaps are 

identified which would need to be addressed to improve the model’s validity. 

 

Keywords: Genetic Algorithms, Pump scheduling, Optimization, EPANET, Energy Efficiency, Hydraulic 

simulation, Python, Water Distribution System, Setpoint curve, Water Tank Level. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



V 
 

 

 

 

Acknowledgements 
 

I would like to express my sincere gratitude to my supervisors at Kretslopp och Vatten for 

the opportunity to undertake this thesis and for their continuous support, inspiration, and 

guidance provided throughout the process. I am also thankful for providing access to data 

and software resources that enabled the completion of this thesis. 

I am also grateful to Andreas Hermanson at Kretslopp och Vatten for his assistance and 

guidance in the hydraulic modelling aspects.  

Finally, I would like to thank Thomas Pettersson at Chalmers University of Technology for his 

supervision and for serving as an examiner. 

Alvar Wikström, Gothenburg, June 2025 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



VI 
 

Contents 
Abbreviations ......................................................................................................................................................... IX 

List of Figures .......................................................................................................................................................... X 

List of Tables.......................................................................................................................................................... XII 

1. Introduction .................................................................................................................................................... 1 

1.1 Purpose ................................................................................................................................................ 2 

1.2 Scope .................................................................................................................................................... 2 

1.3 Limitations and Delimitations .............................................................................................................. 2 

1.3.1 Demand representation .................................................................................................................. 2 

1.3.2 Control approach ............................................................................................................................ 2 

1.3.3 Optimization method ...................................................................................................................... 2 

1.3.4 Electricity price as a “pseudo” variable ........................................................................................... 3 

1.4 Water distribution networks ................................................................................................................ 3 

1.4.1 Hydraulic pressure zones ................................................................................................................ 3 

1.4.2 Water tanks and reservoirs ............................................................................................................. 4 

1.4.3 Pressure levels ................................................................................................................................. 5 

1.5 Demand curves/patterns ..................................................................................................................... 5 

1.5.1 Water demand ................................................................................................................................ 5 

1.5.2 Energy demand/production ............................................................................................................ 6 

2. Literature study .............................................................................................................................................. 7 

2.1 Optimization......................................................................................................................................... 7 

2.1.1 Deterministic models ...................................................................................................................... 7 

2.1.2 Metaheuristic models ..................................................................................................................... 7 

2.2 Genetic Algorithms .............................................................................................................................. 8 

2.2.1 Structure.......................................................................................................................................... 8 

2.2.2 Population and Initialization ........................................................................................................... 9 

2.2.3 Encoding .......................................................................................................................................... 9 

2.2.4 Fitness ............................................................................................................................................. 9 

2.2.5 Operators ........................................................................................................................................ 9 

2.3 Objective function .............................................................................................................................. 11 

2.4 Decision variables .............................................................................................................................. 12 

2.4.1 Pump status ................................................................................................................................... 12 

2.4.2 Tank Trigger levels ......................................................................................................................... 12 

2.5 Constraints ......................................................................................................................................... 12 

2.5.1 Constraints vs penalties ................................................................................................................ 12 

2.6 The use of hydraulic models .............................................................................................................. 13 

2.7 Real world implementation ............................................................................................................... 13 

2.8 Trigger level control ........................................................................................................................... 14 



VII 
 

2.9 Setpoint-curve control ....................................................................................................................... 16 

3. Method ......................................................................................................................................................... 19 

3.1 Software ............................................................................................................................................. 20 

3.1.1 EPANET .......................................................................................................................................... 20 

3.1.2 EPyT ............................................................................................................................................... 20 

3.1.3 DEAP .............................................................................................................................................. 21 

3.1.4 MIKE+ ............................................................................................................................................ 21 

3.2 Hydraulic models ............................................................................................................................... 21 

3.2.1 NET-1 ............................................................................................................................................. 21 

3.2.2 HPZ-G............................................................................................................................................. 22 

3.3 Validation of the HPZ-G hydraulic model ........................................................................................... 22 

3.3.1 Pump curve calibrations ................................................................................................................ 22 

3.3.2 Hydraulic simulation validation ..................................................................................................... 23 

3.4 Timesteps ........................................................................................................................................... 23 

3.4.1 Hydraulic timestep ........................................................................................................................ 23 

3.4.2 Reporting timestep ........................................................................................................................ 23 

3.4.3 Rule timestep ................................................................................................................................ 23 

3.4.4 Interpolation interval timestep ..................................................................................................... 23 

3.5 Objective function .............................................................................................................................. 24 

3.5.1 Energy cost .................................................................................................................................... 24 

3.5.2 Constraints .................................................................................................................................... 24 

3.6 The Optimization algorithm ............................................................................................................... 27 

3.6.1 Key-parameter encoding ............................................................................................................... 27 

3.6.2 Pump trigger ranges variable ........................................................................................................ 29 

3.6.3 Mutation scheme .......................................................................................................................... 30 

3.6.4 Initialization Scheme ..................................................................................................................... 32 

3.6.5 Crossover Scheme ......................................................................................................................... 32 

3.6.6 Elitism Strategy .............................................................................................................................. 33 

3.6.7 Selection strategy .......................................................................................................................... 33 

3.6.8 Parallelization ................................................................................................................................ 33 

3.6.9 Hyper-parameter strategy ............................................................................................................. 34 

3.7 Scenario evaluations .......................................................................................................................... 34 

3.7.1 NET-1 ............................................................................................................................................. 34 

3.7.2 HPZ-G............................................................................................................................................. 35 

4. Data .............................................................................................................................................................. 36 

4.1 Electricity price ................................................................................................................................... 36 

4.2 Suction pressure from the general WDS ............................................................................................ 36 

4.3 Hyperparameters ............................................................................................................................... 36 



VIII 
 

5. Results .......................................................................................................................................................... 38 

5.1 Validating the HPZ-G hydraulic model ............................................................................................... 38 

5.1.1 Pump curve calibrations ................................................................................................................ 38 

5.1.2 Simulating current control scheme ............................................................................................... 40 

5.1.3 Pump station 2 .............................................................................................................................. 42 

5.2 Net1.................................................................................................................................................... 42 

5.2.1 Parallelization ................................................................................................................................ 42 

5.2.2 Simple optimization scenario ........................................................................................................ 43 

5.3 HPZ-G ................................................................................................................................................. 44 

5.3.1 Timestep Sensitivity Analysis......................................................................................................... 44 

5.3.2 Main HPZ-G optimization results .................................................................................................. 46 

5.3.3 Scenario 2022-11-07 ..................................................................................................................... 46 

5.3.4 Scenario 2022-11-13 ..................................................................................................................... 47 

6. Discussion ..................................................................................................................................................... 49 

6.1 Control scheme/Real network ........................................................................................................... 49 

6.1.1 Validity of hydraulic model ........................................................................................................... 49 

6.1.2 Validity of Energy data .................................................................................................................. 49 

6.1.3 Objective function development ................................................................................................... 49 

6.2 Optimization algorithm ...................................................................................................................... 49 

6.2.1 Shortcoming of the algorithm ....................................................................................................... 49 

6.2.2 Pump trigger ranges ...................................................................................................................... 50 

6.2.3 Timestep variables ........................................................................................................................ 50 

6.2.4 Parallelization ................................................................................................................................ 50 

7. Conclusion and further development .......................................................................................................... 51 

7.1 Conclusion .......................................................................................................................................... 51 

7.2 Further improvement for optimization model................................................................................... 51 

7.3 Recommendation of the current control scheme .............................................................................. 52 

References ............................................................................................................................................................. XI 

Appendix .............................................................................................................................................................. XIII 

A - Electricity prices .............................................................................................................................................. XIII 

B - Water Demand data ....................................................................................................................................... XIV 

C – General HPZ-G Run hyperparameters ............................................................................................................. XV 

D – PS-2 Results from validation of hydraulic model 2022-11-07 ........................................................................ XVI 

E – Truncated Fourier series encoding ............................................................................................................... XVIII 

 

 



IX 
 

Abbreviations 
 

GA  Genetic Algorithm 

HPZ  High Pressure Zone 

TLC  Trigger Level Control 

FSP  Fixed Speed Pumps 

WDS  Water Distribution System 

WST  Water Storage Tank 

mWC  Meter Water Column 

SCADA  Supervisory Control and Data Acquisition 

KoV  Kretslopp och vatten, Göteborg stad 

PTR  Pump Trigger Ranges 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



X 
 

List of Figures 
 

Figure 1-1 Illustration of simple boosted HPZ ......................................................................................... 3 

Figure 1-2 Topographic map of Gothenburg ........................................................................................... 4 

Figure 1-3 Typical residential are-based demand consumption pattern. ............................................... 5 

Figure 2-1 Overview of optimization schemes relevant for water pump optimization .......................... 8 

Figure 2-2 Illustration of basic genetic algorithm terminology ............................................................... 9 

Figure 2-3 Example of a simple single-point crossover operation. ....................................................... 10 

Figure 2-4 Example of a simple mutation operation. ............................................................................ 10 

Figure 2-5 Illustration of a tournament-based selection process. ........................................................ 11 

Figure 2-6 Visualization of the solution space in a constrained optimization problem. ....................... 13 

Figure 2-7 Illustration of FTLs scheme, Adapted from (Quintiliani & Creaco, 2019) ............................ 14 

Figure 2-8 Illustration of RFTLs scheme, Adapted from (Quintiliani & Creaco, 2019) .......................... 15 

Figure 2-9 Illustration of VTLs scheme, Adapted from (Quintiliani & Creaco, 2019) ............................ 15 

Figure 2-10 Illustration of RFLATSs scheme, Adapted from (Quintiliani & Creaco, 2019) .................... 16 

Figure 2-11 Simple setpoint curve illustration. ..................................................................................... 16 

Figure 2-12 Illustration of a set-point curve with individual pump-specific threshold ranges. ............ 17 

Figure 3-1 Flow diagram of complete optimization scheme. ................................................................ 20 

Figure 3-2 Hydraulic representation of the NET-1 network. ................................................................. 21 

Figure 3-3 Simplified schematic overview of the studied HPZ, referred to a “HPZ-G” ......................... 22 

Figure 3-4 Illustration of the effect Interpolation interval timestep ..................................................... 24 

Figure 3-5 Schematic overview of EPANET error/warning handling. .................................................... 26 

Figure 3-6 Schematic overview of the encoding–decoding process used in the genetic algorithm. .... 27 

Figure 3-7 Visual representation of the key-parameters. ..................................................................... 28 

Figure 3-8 Example of pump threshold ranges (pt_var = 1) .................................................................. 29 

Figure 3-9 Pump threshold ranges after scaling by pt_var = 0.5 ........................................................... 29 

Figure 3-10 setpoint curve vs actual reservoir level, real-world data from 2022-11-07 ...................... 30 

Figure 3-11 Visual representation of the Peak-Dip separation constraint ............................................ 32 

Figure 3-12 Visual representation of the block-based crossover scheme. ........................................... 32 

Figure 3-13 Schematic overview of the parallel evaluation process using a “master-slave” method. . 33 

Figure 3-14 Tariff periods and initial (unoptimized) setpoint curve ..................................................... 34 

Figure 5-1 Operating points for pumps in Pump Station 1 for the HPZ-G network. ............................. 38 

Figure 5-2 Recreated pump curves based on actual operating points in Pump Station 1 .................... 39 

Figure 5-3 Operating points for pumps in Pump Station 1 for the HPZ-G network. ............................. 39 

Figure 5-4  Recreated pump curves based on actual operating points in pump station 2 ................... 40 

Figure 5-5 Actual WTL measured in the simulation and from real-world data. .................................... 40 

Figure 5-6 Outgoing flow from PS-1 measured in the simulation and from real-operation data. ........ 41 

Figure 5-7 Outgoing pressure from PS-1 measured in the simulation and from real-world data. ....... 41 

Figure 5-8 Active pumps in the simulation and during the real-world scenario. .................................. 42 

Figure 5-9 Runtime as a function of the number of processes used for parallel evaluation. ............... 42 

Figure 5-10 Evolution of reservoir level set-point curves over nine generations. ................................ 43 

Figure 5-11 Comparison of initial and optimized set-point curves ....................................................... 44 

Figure 5-12 Impact of reporting timestep on average runtime and energy cost .................................. 44 

Figure 5-13 Impact of hydraulic timestep on average runtime and accuracy ...................................... 45 

Figure 5-14 Impact of interpolation timestep on average runtime and energy cost ............................ 45 

Figure 5-15 Optimized reservoir level and base solution for the 24-hour time period: 2022-11-07.... 46 



XI 
 

Figure 5-16 Optimized reservoir level and base solution for the 24-hour time period: 2022-11-13.... 47 

Figure B-1 Water demand per hour for 2022-11-07 ............................................................................ XIV 

Figure B-2 Water demand per hour for 2022-11-13 ............................................................................ XIV 

Figure D-1 Outgoing flow from PS-2 measured in the simulation and from real-operation data. ...... XVI 

Figure D-2 Outgoing flow from PS-2 measured in the simulation and from real-operation data. ...... XVI 

Figure D-3  Active pumps in the simulation and during the real-world scenario ............................... XVII 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



XII 
 

List of Tables 
 

Table 2-1 Start and stop thresholds for pumps relative to the set-point curve ................................... 17 
Table 3-1 Description of variables in the key-parameter encoding scheme. ........................................ 27 
Table 3-2 Clipping bound for key parameters ....................................................................................... 31 
Table 3-3 Timestep variables for "baseline scenario" ........................................................................... 35 
Table 4-1 General GA Settings ............................................................................................................... 36 
Table 4-2 Penalty variables ................................................................................................................... 36 
Table 4-3 Crossover weighting variables ............................................................................................... 37 
Table 4-4 Timestep variables ................................................................................................................. 37 
Table 4-5 Mutation probability variables .............................................................................................. 37 
Table 4-6 Mutation Clip bound variables .............................................................................................. 37 
Table 5-1 Summary potential cost savings during the evaluated timeframe. ...................................... 46 
Table 5-2 Key-parameter encoded genotype for optimized setpoint curve ......................................... 47 
Table 5-3 Key-parameter encoded genotype for optimized setpoint curve ......................................... 48 
Table A-1 Electricity prices for 2022-11-07 .......................................................................................... XIII 
Table A-2 Electricity price for 2022-11-13 ............................................................................................ XIII 
Table C-1 Hyperparameters for general HPZ-G run. ............................................................................. XV 
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



1 
 

 

1. Introduction 
 

The water distribution system (WDS) constitutes a vital component of critical drinking water 

infrastructure. Such systems inherently require high reliability due to clean water’s foundational role 

in modern society. For most drinking water systems, raw and drinking water pumping constitutes 

most of the energy use (Tarek et al., 2022). Conditions such topology and consumption patterns can 

have great effects on the required infrastructure and operating cost. Recent times also seem to 

suggest that prices and tariffs for electricity is on the rise (Hagman et al., 2024). The energy system is 

also turning more electrified and reliant on variable renewable energy sources. The demand for 

flexible, smart energy consumption is increasing. Recent periods of fluctuating prices of electricity 

have also further increased interest in consumption flexibility in WDS. It is important to note that the 

main objective of water distribution is quality and reliability.  

A great deal of research has gone into optimizing the operation of water distribution to minimize its 

operational cost. The methodology of these studies can roughly be divided into rule-based control 

schemes and optimization algorithm-based methods (Giustolisi et al., 2013). A rule-based control 

scheme essentially means to use fixed control rules to control pumps. For example, a pump turns on 

when the water tank level is low, and off when it is full. It is a simple method to implement, and it 

responds in real time to current system status. It does however have limited optimization 

opportunities. Optimization-based methods use advanced algorithms to find the optimal schedule for 

operating pumps, often considering several different objectives. These objectives usually include 

energy cost, maintenance cost and reliability. These methods have the potential to provide more 

flexible and cost-effective scheduling compared to simple rule-based controls. These models are 

however: more complex, harder to implement and require accurate predictions of future demand, 

electricity tariffs and system response (Salomons & Housh, 2020). 

This thesis aims to incorporate different aspects of both methods. The idea of a rule-based control 

optimization has been put into use before. For example, Marchi et al., (2017) implement and 

optimize flexible rule-based pump controls by including multiple conditions. These conditions where 

for example: tank levels, time-of-day, and pump status. This enhanced control logic is coupled with a 

genetic algorithm that tunes rule parameters to minimize energy costs while maintaining hydraulic 

stability in the system. Alvisi & Franchini, (2017) propose a trigger level-based strategy for pump 

control. Using a multi-objective genetic algorithm, they optimize these trigger levels to balance 

energy cost and the number of pump switches. While having some similarities with the approaches 

discussed in these articles, this thesis offers an alternative way to constrict and traverse the solution 

space. The optimization method proposed in this thesis is based on a setpoint curve control scheme. 

In the field of control theory, a setpoint curve refers to a predefined time-varying target value which 

a control system aims to maintain. Which in this specific scenario would be the level in the water 

tank, controlled by switching pumps on/off. This control scheme is described in detail in section 2.10.  

The main novelty of this thesis is the setpoint curve specific optimization approach. In this 

optimization scheme the set-point curve is encoded by a few key parameters. New solutions are then 

generated through mutating these key-parameters which provide meaningful changes of the set-

point curve. These changes are introduced based on a GA based optimization scheme. An extensive 

description of the optimization scheme is available in the method section.  



2 
 

The genetic algorithm is implemented using the DEAP evolutionary framework (Fortin et al., 2012), 

and candidate control curves are evaluated through EPANET simulation. The core idea of 

optimization is to reduce energy cost whilst respecting operational constraints such as reservoir 

bounds, pressure requirements, pump switching and demand security. 

1.1  Purpose  
The purpose of this thesis is to develop and evaluate an optimization framework for energy-efficient 

pump scheduling in water storage tank-based water distribution network. This approach aims to 

strike a practical balance between rule-based, interpretable control strategies and modern 

optimization techniques. 

The proposed control scheme will be validated through simulation on a real-world water distribution 

network that has been calibrated using historical operational data. Performance will be assessed by 

comparing the optimized solutions generated by the genetic algorithm with the existing control 

strategy. This comparison will highlight potential improvements in energy efficiency, constraint 

handling, and adaptability introduced by the optimization-based approach. 

1.2  Scope  
The optimization framework is applied to a hydraulically isolated high-pressure zone within a larger 

water distribution system. This delimitation was made to reduce model complexity, limit simulation 

runtimes, and improve calibration accuracy given the available operational data. More broadly, raw 

water pumping and the energy required for water treatment are excluded from the analysis. As a 

result, the optimization focuses exclusively on a specific part of the clean water distribution stage, 

where electricity costs with pump operations are most significant and directly controllable. 

1.3  Limitations and Delimitations 

1.3.1 Demand representation 
The consumption patterns used for simulations and evaluation are derived from historical operating 

data from a limited time period. As such the optimization results will be true for the investigated 

time period, but the result could vary significantly for time periods with different consumption 

patterns. 

1.3.2 Control approach 
This thesis deliberately focuses on optimizing a smooth set-point curve that implicitly controls when 

pumps turn on/off rather than performing explicit pump scheduling. This choice was mainly 

motivated by the desire to create an optimization scheme, fully compatible with the current control 

scheme. The set-point curve approach also enables a smoother incorporation of domain knowledge, 

used to generate a more efficient and targeted optimization process. More explicit pump scheduling 

has the potential of increased energy savings (Quintiliani & Creaco, 2019). However, it is generally 

harder to apply in practice as it substantially increases the complexity of the application. It often 

depends heavily on accurate short-term demand forecasts, which are not always available or reliable 

in practice (Salomons & Housh, 2020). 

1.3.3 Optimization method  
A wide range of optimization methods are relevant to pump scheduling, including linear 

programming based, mixed-integer models, and metaheuristics approaches. This thesis focuses on 

Genetic Algorithms (GAs), motivated by the demonstrated effectiveness in existing pump scheduling 

studies (Mala-Jetmarova et al., 2017). GAs is particularly well-suited for non-linear, non-convex, and 



3 
 

constraint-heavy problems (Nicklow et al., 2010), characteristics that are typical of real-world water 

systems (Marchi et al., 2017). The traditional mutation and crossover operators also synergies well 

with the encoding scheme utilized in this thesis. These operators are described in more detail in 

Chapter 2. 

1.3.4 Electricity price as a “pseudo” variable  
In this thesis, the electricity price is treated as a simplified proxy for the wider, more complex 

electricity tariff components. Rather than modeling the detailed structure of grid fees, capacity 

charges, power-based demand tariffs, and other contractual elements, the optimization scheme 

considers only the unit energy price. This was done partly since the specific tariff scheme paid by 

Kretslopp och vatten, Göteborg stad was not a central part of the research question, and the main 

objective was to create an optimization algorithm adapted for the specific control system. Focusing 

only on the energy price still captures the main operation incentives: shifting pump usage from high 

price/demand periods to reduce cost and grid load. 

1.4  Water distribution networks 

1.4.1 Hydraulic pressure zones 
A hydraulic pressure zone (HPZ) can be defined as delimited part of the WDN for which obtains a 

certain pressure gradient (Salomons & Housh, 2020). These zones are thus connected to the general 

WDN through some type of pressure control device, such as a pumping station or a pressure 

reducing valve. HPZs are established based on elevation differences in the WDN, higher elevations 

require more pumping to reach desired pressure, and lower elevation might require Pressure 

reducing valves to not reach too high-pressure levels. In figure 1-1 a simple illustration of a boosted 

HPZ can be seen. 

 

 

Figure 1-1 Illustration of simple boosted HPZ 

 

The dotted line represents the Hydraulic Gradient Line (HGL), it’s a common concept in fluid 

dynamics and represents the pressure head and the elevation head. The figure presents an idealized 



4 
 

case that neglects friction losses, which would otherwise make the line more slanted. Larger WDN 

can contain multiple HPZs, the amount is mainly determined by topological conditions. Figure 1-2 

presents an elevation map of the Gothenburg region. The distinct topographical variation clearly 

indicates the necessity of high-pressure zones in certain areas to maintain suitable pressure levels. 

 

 

Figure 1-2 Topographic map of Gothenburg generated from TessaDEM data (v1.2) (TessaDEM, 2025) 

 

A large amount of HPZs is operated with a Water Storage tank (WST), which offer more flexibility and 

reliability. HPZ can also be operated without storage, directly via pumping stations. These zones are 

referred to as “rigid” and are in most cases operated with variable speed pumps (VSP). 

1.4.2 Water tanks and reservoirs  
In the context of water distribution networks, the terms tank and reservoirs are often used quite 

interchangeably. However, in the context of simulation software (such as EPANET), a distinct 

difference exists between the two terms. A reservoir represents an infinite source or sink with a 

specified hydraulic head. The hydraulic head can be fixed or specified by a predetermined pattern. 

The flow from/to the reservoir is essentially determined by the pressure difference between the 

reservoir and the connected network. A tank on the other hand represents a finite-volume storage, 

where to volume depends on the inflow/outflow. The pressure head will thus calculate at every 

timestep, based on the tank volume. In this thesis the terms are used interchangeably. 

The main purposes of WST are to provide increased reliability and flexibility. This is done mainly by 

storing water during low demand periods and supply it when demand is high. This cycling is usually 



5 
 

done on a daily time horizon, e.g. filling reservoir at night and emitting most of it during the day. 

Without WST, pumps in HPZ will have to run all the time, constantly adjusting the output based on 

the current demand. A WST enables limited and stable pump operation during high demand periods. 

WST also enable pumping to complete stop, while still maintaining pressure in the network. This is 

especially useful during maintenance and in case of pump failure.  

1.4.3 Pressure levels 
Correct management of high-pressure zones (HPZ) minimizes excessive pressure levels, thereby 

reducing pumping costs and lowering the risk of leakages and pipe bursts (Creaco et al., 2019). At the 

same time, it is essential to always ensure adequate pressure on customer nodes. Industry standards 

recommend a minimum pressure of 15 meters of water column (mWC) above the highest outlet at 

the connection site, while the maximum recommended pressure is 70 mWC (Svenskt Vatten, 2021). 

1.5  Demand curves/patterns 
In ordered to optimize pump scheduling a certain understanding of how the water demand varies 

over time is needed. In terms of energy optimization, it is also important to have a basic 

understanding of energy demand and production patterns.  

1.5.1 Water demand 
Consumption will vary based on time of year and temperature/weather, but the general shape of the 

consumption tends to stay the same. The type of consumer will also affect the shape of the demand. 

For example, an industry’s water consumption generally increases more during the day and can have 

less predictable patterns due to different water intensive processes. In this thesis the focus will be on 

a more residential based demand curve as this is the main type of consumer in investigated HPZ and 

is also representative of most of the demand in the Gothenburg Water distribution network. 

In figure 1-3 a water consumption pattern can be seen for a typical weekday. Two demand peaks can 

be seen during the morning and afternoon, whilst a very low consumption can be seen during the 

night. During weekends, water consumption typically decreases and is slightly delayed. 

 

 

Figure 1-3 Typical residential are-based demand consumption pattern. 

 



6 
 

1.5.2 Energy demand/production 
Electricity price tends to be a good surrogate for capturing both energy demand and production. The 

main pricing mechanism in Sweden is the day-ahead market run by Nord Pool (Hagman et al., 2024). 

Hourly prices are set the day before based on bidding by electricity producers and retailers. Even if a 

municipal electricity consumer often holds more fixed-price based electricity contract, there is still 

merited to considering real-time electricity prices. For example, grid fees, capacity charges, and 

power-based tariffs are generally not affected by a fixed electricity price. Also, by aligning operation 

with lower-priced periods, these types of consumers could assist in offloading the grid during high 

consumption periods, thus improving grid stability and efficiency (Hagman et al., 2024).  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



7 
 

2. Literature study 
 

2.1  Optimization 
An optimization algorithm essentially is a method used to find the best solution from a set of 

potential solution. What constitutes a best solution is based on single or multiple pre-determined 

objectives. When considering the choice of optimization method, it can be good to consider the “No 

Free Lunch Theorem”. This theorem essentially states that there is no overall superior optimization 

algorithm that can solve all problems, and that a method efficient for a specific set of problems will 

be outperformed by other algorithms on different set of problems (Kramer, 2017). At its core, 

optimization is about finding the most suitable method for the problem at hand and adjusting the 

method to obtain a solution as efficiently and accurately as possible. In the context of WDS 

optimization, the optimization methods can generally be divided into two different categories: 

Deterministic model and heuristic/metaheuristic models.  

2.1.1 Deterministic models  
Deterministic models follow a systematic predictable process to determine results. For any given 
output the result from the model will always be the same. Examples of deterministic methods: Linear 
programming (LP), nonlinear programming (NLP), Mixed-Integer Linear Programming (MILP). These 
models are reliable, provide mathematically precise solutions and are efficient for well defined, 
structured problems (Sivanandam & Deepa, 2008). The drawback can however be that deterministic 
methods can struggle with large or complex networks due to computational limitations, and for non-
convex problems they can end up in local optima (Balekelayi & Tesfamariam, 2017). These models 
are also arguably less suited of handling multi objective functions as the ability to manage complex 
trade-offs and explore diverse solutions is limited.  
 

2.1.2 Metaheuristic models  
Technologic advancements improving the efficiency of hydraulic simulations and computational 

speed in general, has made non-deterministic metaheuristic models more attractive (Mala-Jetmarova 

et al., 2017). These methods do not depend on gradients (derivatives) when searching for the 

optimal solution (Balekelayi & Tesfamariam, 2017). Instead, it is a higher-level procedure which aim 

to find a good enough solution based on some type of general heuristic method rather than a specific 

mathematic formula. A common attribute for metaheuristic models, especially in the field of WDS is 

that they are population based. This means they maintain and evolve a set of potential solutions 

simultaneously. They can also be applied to large-scale water networks with high-dimensional 

decision spaces (Janga Reddy & Nagesh Kumar, 2020). These models can balance exploration 

(searching the solution space) and exploitation (refining promising solutions).  

It is naturally important to take the optimization model into consideration when defining the 

optimization objective. Deterministic models require more strict variable bounds and relationships. 

Metaheuristic models can handle more “soft” constraints, conflicting objective functions. In figure 2-

1 an overview of optimization methods relevant to pump scheduling optimization can be seen. 

 
 



8 
 

 
Figure 2-1 Overview of optimization schemes relevant for water pump optimization 

 

2.2  Genetic Algorithms  
Genetic algorithms are a type of metaheuristic method for solving optimization problems, inspired by 

the biological process of natural selection. It is part of the larger class of Evolutionary algorithms. 

These algorithms imitate how populations evolve over generations using mechanisms such as 

crossover, mutation, and selection. GA is well established in the field of pump scheduling 

optimization, and many different applications are available in literature (Mala-Jetmarova et al., 

2017). A great advantage of GAs is that it does not rely on gradient information, making it more 

suitable for problems where the relationship between decision variables and the objective function 

are more complex.  

2.2.1 Structure 
In its simples form a Genetic algorithm is built upon chromosomes which are represented by a string 

of binary values (1,0). These individual values are referred to as genes and can represent some type 

of action/operation, for example pump on/off statuses.  A group of chromosomes is referred to as a 

population. In figure 2-2 a simple illustration of structures can be seen.  



9 
 

 

Figure 2-2 Illustration of basic genetic algorithm terminology 

2.2.2 Population and Initialization 
A population consists of a group of individuals, where each individual represents a solution. An 

important variable for GA is the size of the population. This variable will depend on the complexity of 

the problem and how the solution is structured (Sivanandam & Deepa, 2008). The initial population is 

often generated through some type of random initialization. For many problems the first population 

should ideally contain a wide array of solutions, to be able to capture the entire solution space. It is 

also possible to utilize heuristics to generate an initial population which has a higher average fitness 

value. This can be useful to obtain faster conversion rates but could also increase the risk of ending 

up in a local optimum. In the context of trigger levels, it is reasonable to use a heuristic initialization 

to obtain an initial solution which consists of mostly feasible solutions.  

2.2.3 Encoding  
For many problems, the actual solution is quite complex and needs to be discretized to be 

compatible with the different genetic operators. Expressing the solution as simpler data structure 

ensures that the model operates efficiently and accurately. Usually, the actual solution is referred to 

as the phenotype and the encoded representation of the solution is referred to as the genotype 

(Sivanandam & Deepa, 2008). To evaluate each solution, a conversion from genotype to phenotype is 

done as a part of the fitness function.  

2.2.4 Fitness 
The fitness functions essentially evaluate the quality of each solution, based on the desired 

objective/objectives. For multiple objective optimization the fitness function can be more complex to 

express. The fitness function is essentially equivalent to the objective function, which is discussed in 

the following section. 

2.2.5 Operators 
Operators are the mechanisms which determine the evolution of populations over multiple 

generations. In this section the general methodology for these operators will be covered, the specific 

operators used in the actual model and the motivation for using these are available in the method 

section. 



10 
 

Crossover  
The operator which combines genetic material from two or more solution chromosomes (parents) to 

form a new solution (child) (Kramer, 2017). In its simplest form this can be done by a “single-point 

crossover” which can be seen in figure 2-3. A crossover point is selected somewhere along the 

chromosome. The string on each side of the point will come from different parents.  

 

Figure 2-3 Example of a simple single-point crossover operation. 

Mutation 
The main purpose of mutations is to introduce genetic diversity through random changes of the 

populations. This in turn will prevent premature convergence and assist the algorithms in avoiding 

getting stuck in local optima. For a binary chromosome string a simple mutation could simply be 

randomly switching a gene from 0 to 1 (or vice versa). This is referred to as Bit-Flip mutation and can 

be seen in figure 2-4.  

 

 

Figure 2-4 Example of a simple mutation operation. 

Selection 
Is the process which selects the best offspring solutions based on the previously mentioned fitness. 

This is essentially what decides which solutions are chosen for each new generation. Most selections 

employ some selection strategy based on fitness in combination with some type of randomness. A 

balance between exploration and exploitation is often desirable. A common selection method used is 

tournament selection. In this method n amount of solutions are chosen at random. The solution with 

the bests fitness value is then selected for the next generation, whilst the others are discarded. A 

greater n increase exploitation. A tournament selection scheme can be seen in figure 2-5. 

 



11 
 

 

Figure 2-5 Illustration of a tournament-based selection process. 

 

Termination 
The condition for termination defines when the evolutionary algorithms should stop. In most cases 

the optimal solution is unknown, therefore the termination condition is rarely based on proximity to 

the optimal solution. Instead, the termination is often based on a predefined number of generations, 

or a lack of improvement from the convergence.   

Heuristic choice of operators  
While many of the GA operators can be applied to a range of different problems, the performance 

will increase drastically if operators design more specific tasks (Sivanandam & Deepa, 2008). As with 

any other optimization algorithm, utilizing information about the domain is an essential part of fine-

tuning the model. Infeasible solutions can be discarded at an early stage of evaluation or even be not 

generated at all.  

2.3  Objective function 
The objective function is an essential part of any optimization algorithm, it essentially decides the 

aim of the optimization model. In the context of Pump scheduling optimization, the most common 

objectives are related to cost minimization, for example: minimization of Energy costs. Objective 

functions with multiple goals are referred to as multi-objective. Other objectives which can also be 

addressed are water quality constraints and security of supply. These types of objectives can be 

harder to quantify and is therefore often defined as constraints. Ideally all elements of an objective 

function should be expressed as the same unit, to obtain an optimal solution. In multi-objective 

optimization, the objectives can often be conflicting. If the objective function uses different units, the 

optimization results will be in the form of a pareto front. A pareto front represents a set of non-

dominated solutions. Non-dominated essentially just means that each solution cannot be improved 

based on any objective, without worsening another objective (Kramer, 2017).  

 

 

 



12 
 

2.4  Decision variables  
The controllable elements and actions of the system which are to be optimized by the model. These 

can both be in the form of binary- or continuous values. 

2.4.1 Pump status 
These are binary values which indicates if a pump is on or off. In this model the pump statuses are 

implicit variables as they are directly controlled by the trigger levels of the tanks. In this model all 

pumps are assumed to be Fixed Speed Pumps.  

2.4.2 Tank Trigger levels 
The tank trigger levels are the main controlling variable for the model. In its simplest form tank 

trigger levels are constant and set as the actual maximum/minimum levels of a tank (Quintiliani & 

Creaco, 2019). Dynamically changing trigger levels will vary throughout the day, changing the span of 

allowable reservoir levels. 

2.5  Constraints 
The limitations of the systems and requirements which must be fulfilled while performing the 

optimization are referred to as constraints. They can represent hydraulic constraints such as 

restriction of flow in pipes and mass balance in a tank. System constraints refer to limitations set by 

the specific system such as: max/min levels in reservoirs and required pressures for specific nodes. 

Operational constraints can be defined as an operation limit set by the system, for example: amount 

of pump switches. Certain elements of the objective function can express constraints.  

2.5.1 Constraints vs penalties 
In the context of optimization algorithms, particularly in Genetic algorithms, undesirable features of 

solutions can be handled in two main ways. One of the most basic methods is the death penalty, 

which essentially represent expressing something as a hard constraint. In a death penalty regime, any 

solution which violates any constraint is discarded (Kramer, 2017). For some problems, it can be 

favorable to immediately discard unfeasible solutions and not waste any resources on computing any 

derivatives of these undesirable solutions. An example could be violations which could lead to 

inaccurate results or crashes in the simulation’s software. However, for a lot of problems the optimal 

solution will reside near the unfeasible region of solutions. As such there is a great incentive to 

extract information from these infeasible solutions (Sivanandam & Deepa, 2008). Penalty functions 

are a way to handle infeasible solutions as opposed to discarding them entirely. The fitness value is 

instead reduced based on the severity of the violation. To be effective, the penalty unit costs must be 

sufficiently high to guide the algorithm toward viable solutions, but not so high that they exclude 

potentially good alternatives (Abdelsalam & Gabbar, 2021). As with most other hyperparameters in 

genetic algorithms, the penalty factors are problem specific and need to be calibrated based on the 

structure of the optimization.  

Figure 2-6 illustrates the somewhat abstract concept of a solution space. If infeasible solutions are 

simply discarded, those near the feasible region offer no value. By instead applying penalty functions, 

these nearby infeasible solutions can help guide the search toward feasible ones - a key advantage in 

stochastic optimization methods like Genetic Algorithms. 

 



13 
 

 

Figure 2-6 Visualization of the solution space in a constrained optimization problem. 

 

2.6   The use of hydraulic models 
In the context of pump scheduling optimization, EPANET hydraulic simulations are commonly used, 

though they can be applied in several different ways. The hydraulic model is used in combination 

with some type of optimization model. One way to incorporate these is to generate different pump 

schedules with the optimization algorithm and then using the hydraulic simulation to verify its 

feasibility in terms of mass balances and pressure requirements (Van Zyl et al., 2004). Some models 

will also operate iteratively to refine optimization model parameters each time step, which leads to 

more extensive computational effort.  

Some methods will also exclude the use of hydraulic simulation tools such as EPANET, instead opting 

for integration of the hydraulic equations directly into the optimization framework (Janus et al., 

2023; Thomas & Sela, 2024). These methods perform approximations and linearization to enable to 

non-linear hydraulic constraints to be solved by more deterministic optimization solvers. These 

methods have the potential to provide guaranteed optimal solutions with lower computational 

processing. However, the drawback being that the simplification of the system naturally introduces 

inaccuracies of the model.  

2.7  Real world implementation 
As mentioned, a clear distinction must be made between an optimizing scheme for scheduling and 

for real time control. Metaheuristics optimizations schemes which utilize hydraulic simulations are 

not efficient enough to be applied in a real time scenario (Balekelayi & Tesfamariam, 2017). 

Another challenge with real world implementation is related to data handling in Supervisory Control 

and Data Acquisition (SCADA) systems. Calculations done inside the SCADA are generally limited to 

simpler programming logic and might not be suitable for complex optimization algorithms. Therefor 

these calculations will have to be done outside the SCADA environment and then be re-entered into 

the system. This type of operations is not trivial, especially not if they rely on data/software from 

outside sources such as electricity prices or commercial optimization algorithms. The options are thus 

to provide a pump schedule or rely on simpler calculation which can be deployed on simpler 

hardware. 

Another challenge with real world applications is that the optimization models sometimes might 

seem like a “black box”, i.e. limited insight in how the algorithm operates. It is important that the 



14 
 

responsible operator understands the control scheme. Control schemes for WDS are often based on 

heuristics methods which has been developed over many years, and it is generally hard to implement 

complete overhauls to automatize and optimize entire operation. A more reasonable approach is to 

utilize continues improvements, allowing operations and the surrounding infrastructure time to 

adapt to the new controls.  

2.8  Trigger level control 
In literature, the most common approach of optimize pump operation is trough explicit pump 

scheduling (Mala-Jetmarova et al., 2017). For pre-determined demand pattern, this type of 

scheduling would be able to achieve the absolute optimal solution. For non-determined demand 

patterns, a perfect prediction model would be required to reach an optimal solution, which would 

require constant updates and recalibrations based on the current demand (Alvisi & Franchini, 2017). 

Depending on the inaccuracy of the prediction model, the schedule obtained through explicit pump-

scheduling could be suboptimal. Another downside of Pump scheduling as an optimization technique 

is its vast amounts of decision variables. For each time step, every individual pump on/off status 

would be a decision variable (Quintiliani & Creaco, 2019). Considering Variable speed pumps (VSP) 

would further increase the amount of decision variables. 

To address these issues, a more robust control scheme is to control pumps on/off statuses based on 

water levels in the reservoir. Trigger level control (TLC) is an implicit control scheme which refers to 

setting specific water levels which automatically switch a pump on or off. In its simplest form two 

constant trigger levels are defined, an upper limit and a lower limit. When the reservoir reaches the 

upper limit the pump stops, and when it reaches the lower limit, the pumps start. This simple control 

scheme is referred to as Fixed Trigger Levels and can be seen in figure 2-7.  

 

Figure 2-7 Illustration of FTLs scheme, Adapted from (Quintiliani & Creaco, 2019) 

In the context of trigger level optimization, more advanced versions of FTL have been developed and 

evaluated. These models are mostly based on optimizing for electricity cost, based on different 

“peak” and “off-peak” time periods. One method is Reduced Fixed Trigger levels (RFTLs) (Marchi et 

al., 2017). In this scheme the off-peak off-trigger level is set to the maximum available level of the 

WST and the on-trigger level is the decision variable which is optimized. In the peak period the 

opposite true: on-trigger level is set to the minimum available level, and the off-level is the optimized 

parameter. The RFTLS scheme can be seen in figure 2-8. 



15 
 

 

 

Figure 2-8 Illustration of RFTLs scheme, Adapted from (Quintiliani & Creaco, 2019) 

A downside with RFTLS is that it does not guarantee to reach the highest allowable reservoir level at 

the end of the off-peak period, and the lowest allowable reservoir level at the end of the peak period 

(Alvisi & Franchini, 2017). It is possible to reduce the allowable tank range during each respective 

periods, but that would be greatly increase the amount of pump switches, which would be 

unfavourable from maintenance point of view. To address this issue Variable Trigger levels was 

introduced. Similarly to RFTLs the off-peak off-trigger value and the peak om-trigger value is set as 

maximum respectively minimum allowable tank level. The difference is that the other trigger levels 

are calculated with a power law, with time as the only variable. During the off-peak period the on-

trigger level varies from the minimum tank level to some determined level T1 (slightly below 

maximum tank level). During the on-peak period the off-trigger level varies from the maximum tank 

level to some determined level T2 (slightly above minimum tank level). A simplification of this 

method was established in (Housh & Salomons, 2019) where a linear relationship was introduced for 

the VTLs which eliminates the need for optimizing the power law for each pump. The linearized 

version of VTLs can be seen in figure 2-9. 

Figure 2-9 Illustration of VTLs scheme, Adapted from (Quintiliani & Creaco, 2019) 

 

In (Quintiliani & Creaco, 2019) a further improved method is introduced which aims to address 1. the 

pump trigger levels temporal based change, and 2. The additional pump switches caused by tank-

filling being affected even at large time periods from the actual tariff change. The main novelty of 

RFLATS is that trigger levels are optimized only close to the actual tariff change, creating an 

additional time slot in each respective tariff period. The method thus both achieves more constant 



16 
 

trigger levels and reduces the amount of pump switches. The RFLATs method can be seen in figure 3-

10.   

Figure 2-10 Illustration of RFLATSs scheme, Adapted from (Quintiliani & Creaco, 2019) 

 

2.9  Setpoint-curve control 
In real world scenarios implementation of TLC is often done though the utilization of a set-point 

curve. In this context, the set-point curve indicates what the reservoir level should be at each time 

step. The setpoint curve control scheme is also what is used at KoV, all will be the main control 

scheme covered in the thesis. The values in the setpoint curve are usually defined on an hourly basis, 

and values in between are then interpolated. I figure 2-11 a simple example of a set-point curve can 

be seen.  

 

 

Figure 2-11 Simple setpoint curve illustration. 

 

Most commonly this type of control scheme also requires a second set of parameters which 

represent the leeway for when pumps should turn on/off. In equation 1.1 the error value (e) is 



17 
 

expressed in terms of setpoint value (SP) and PV process value (PV). Here PV represents the actual 

reservoir level. The allowable range for the error is then to be expressed according to 

Upper Deadspann <  e(t) <  Lower Deadspann. 

 

𝑒(𝑡) = 𝑆𝑃(𝑡) − 𝑃𝑉(𝑡) (2.1) 

 

Thus, the operating schedule based on a set-point curve consist of two sets of variables: the actual 

set-point curve and the allowable variance from said set-point curve. The allowable variance usually 

differs between pumps. So, a different number of pumps will be running depending on how much the 

actual value deviates from the set-point curve. The complete control implementation is illustrated by 

figure 2-12. Here a set-point curve with 2 different pumps can be seen. The specific pump trigger 

ranges (PTR) can be seen in table 2.1. Essentially can this type of scheme be seen as pump specific 

TLC which are constantly updating.  

 

 

 

Figure 2-12 Illustration of a set-point curve with individual pump-specific threshold ranges. 

      

Table 2-1 Start and stop thresholds for pumps relative to the set-point curve (Pump trigger ranges). 

 Start Stop 

P1 0,2 -0,5 

P2 0,3 -0,2 

 

For WDS which contain one or multiple reservoirs, different variations of TLC are widely used in 

practice (Salomons & Housh, 2020). It is generally preferred to explicit pump scheduling as it offers a 

simpler control scheme with fewer decision variables. It is also more suitable for a decentralized 



18 
 

system where the control logic situated in the PLC of the WST or the connected pumping station. The 

general methodology is to generate and attempt to optimize these set-point curves offline, and then 

enter it into the SCADA system (Housh & Salomons, 2019). 

It is important to note that there obviously are downsides to using a trigger level as opposed explicit 

pump scheduling. A trigger level approach essentially trades optimality for more reliable solution. 

The trigger-based approach lacks adaptability, and often a temporal offset occurs between the 

filling/emptying of the tank and the off-peak and peak tariff periods (Alvisi & Franchini, 2017). Which 

in the end results in smaller economic gain. Ultimately, the optimal control scheme for a given 

system will depend on the feasibility of dynamically adjusting the model, the frequency of system 

adjustments, the availability of relevant data, the system's sensitivity, and the extent of its 

fluctuations. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



19 
 

3. Method 
 

Based on the literature review, no existing method was deemed a good fit based on the defined 

problem definition. The goal of this work is essentially to develop a model capable of generating 

setpoint curves from available data that can be directly implemented in the SCADA system. Existing 

methods fail to achieve the necessary balance between rule-based control and optimization-based 

approaches. Although certain trigger level-based strategies show promise, they lack sufficient 

temporal resolution to capture short-term dynamics effectively. Which is an essential requirement 

when optimizing setpoint curves. As previously discussed, a setpoint curve can essentially be viewed 

as a trigger-level scheme with shorter and more continuously varying trigger intervals. 

Other optimization-based methods, while mathematically advanced, come with important limitations 

in this context. Many of these rely on detailed system models and require the problem to be 

reformulated for each specific network setup or tariff structure, making them difficult to reuse or 

adapt. They also often depend on precise predictions of future conditions and need a lot of 

adjustments to perform well. As the system becomes more complex, these methods can become too 

slow or difficult to manage. Moreover, they are not always able to produce the desired output of set-

point curves, which are needed by the existing control system. 

To address these problems, a key-parameter encoded genetic algorithm was developed for 

integration with the current set-point curve-based control scheme. Each setpoint curve is 

represented by a concise set of parameters baseline level, peak/dip timing and amplitude, and three 

curvature descriptors that directly generate the smooth, continuous curves expected by the SCADA 

system. An iterative GA optimization, utilizing EPANET hydraulic simulations for evaluations, evolves 

these parameters to minimize energy costs, reduce pump cycling, and enforce water tank 

constraints. By combining the ease of rule-based curve deployment with the global-search 

capabilities of metaheuristic optimization, this method provides a flexible and practical solution to 

the defined problem. In figure 3-1 a complete schematic of the optimization scheme can be seen.  



20 
 

 

3.1  Software 

3.1.1 EPANET 
EPANET is a commonly used hydraulic simulation software originally developed by the US 

Environment Protection Agency (EPA) in 1994 (Rossman et al., 2002). EPANET 2 is the latest major 

release and is available both as a free stand-alone software, and as an open-source toolkit. Some 

software (such as Mike+) utilizes EPANET as a basis for hydraulic calculations.   

3.1.2 EPyT 
EPyT is an open-source python package which enables a high-level python programming interface for 

EPANET (Kyriakou et al., 2023). It is essentially a wrapper for EPANETS C based API. EPyT is designed 

to support automated modeling, simulation, and control of water distribution networks. Many 

previous articles covering similar in the field of WDS optimization utilizes the EPANET-MATLAB 

Toolkit, which has previously served as the main toolkit in linking the EPANET engine to code and 

computing environments.  

Figure 3-1 Flow diagram of complete optimization scheme.  



21 
 

3.1.3 DEAP 
DEAP (Distributed Evolutionary Algorithms in Python) is a powerful, flexible, and open-source Python 

framework specifically designed for creating and experimenting with evolutionary algorithms (Fortin 

et al., 2012). It supports implementation of evolutionary computation techniques such as genetic 

algorithms, genetic programming, evolution strategies, particle swarm optimization and differential 

evolution. 

3.1.4 MIKE+  
MIKE+ is an integrated modeling platform developed by DHI for the simulation and management of 

water systems (DHI, 2024). It builds upon the EPANET engine, enhancing it with features such as GIS-

based visualization, support for additional boundary conditions, and advanced control options. In this 

study, most modifications and calibrations to the HPZ-G model were performed within MIKE+, 

including adjustments to pump curves and pipe configurations to better align with observed SCADA 

data. MIKE+ was also used as a visualization tool, enabling detailed inspection of model behavior, 

such as flow patterns and pressure distribution across different network regions.  

3.2  Hydraulic models  
Two main hydraulic models were used in the process of developing the optimization model. The  

HPZ-G model was obviously the main focus of this thesis, and naturally the results will mostly relate 

to this hydraulic model. However, a much simpler network model, NET-1 was also used quite heavily 

during the development of the optimization model. 

3.2.1 NET-1  
The initial versions of the model were based on a simple small WDS, known as “NET-1”. This is a 

theoretical network used for testing and is one of the standard networks available in EPANET 

(Rossman et al., 2002). It includes a simple layout consisting of 10 interconnected nodes, 12 pipes, 1 

reservoir, 1 pump and 1 WST. It also contains a simple predefined demand pattern. A visual 

representation of the Net1 model can be seen in figure 3-2.  

 

 

Figure 3-2 Hydraulic representation of the NET-1 network. Generated using EPyT (Kyriakou et al., 2023) 

 



22 
 

Even though the real-world implication based on result from the NET-1 model are limited. These 

results still provide meaningful insight of the optimization algorithm. For the more complex hydraulic 

model the optimization process can be harder to decipher given the complex hydraulic relationship, 

and other data inputs. The NET-1 result essentially provide simple demonstration of how 

optimization algorithm navigates in the solution space. 

3.2.2 HPZ-G 
The hydraulic model which represents the actual HPZ which exist inside the greater Gothenburg 

water distribution network. It contains 2 pumping stations with 3 pumps each and a single WST. The 

Actual real network is obviously more complex and containing around 5500 nodes and links each. 

The demand patterns also contain more complexity as it is based on actual measured consumption in 

the zone. The measured consumption from different consumer is aggregated in different demand 

nodes. The demand pattern for these nodes is then representable for all consumers in these 

aggregated points. Due to security reason the detailed layout of HPZ-G network cannot be shared. 

However, a simple illustration of the network structure can be seen in figure 3-3. 

 

3.3  Validation of the HPZ-G hydraulic model 
To ensure the simulations accurately reflected the real network behavior, the model was validated 

using SCADA data from actual operations. The same control rules implemented in the SCADA system 

were applied to the model to replicate comparable operating conditions. 

3.3.1 Pump curve calibrations  
The pumps operating in HPZ are relatively old, and their efficiency has decreased over years of use. 

As a result, relying on manufacturer-provided efficiency data is not reliable (Bunn & Reynolds, 2009). 

Instead, SCADA data was used to develop updated pump curves for use in the simulation model. The 

data used for generating the new pump curves are based on the targeted simulation period. The 

relevant data which was used was PIU (Pumps in use), Q (flow), POUT and PIN (outgoing/ingoing 

pressure). 

Figure 3-3 Simplified schematic overview of the studied HPZ, referred to a “HPZ-G” 



23 
 

3.3.2 Hydraulic simulation validation 
In this step, the simulation results were compared to measured data from the real network over the 

same time-period, utilizing the same control scheme setup. The complete seven-day period was 

simulated in consecutive 24-hour intervals.  

3.4  Timesteps 
Since the hydraulic model is the base of the optimization process, naturally the parameters will 

influence the results. In this section a brief explanation of some relevant timestep parameters will be 

presented, and their effect. In the result section a sensitivity analysis on how the different timesteps 

effects runtime is presented.   

3.4.1 Hydraulic timestep 
The hydraulic timestep determines the time interval between calculations of the hydraulic state of 

the network (Rossman et al., 2002). So essentially how often flows, pressures, tank levels etc. are 

updated. Generally speaking: a smaller hydraulic timestep provides a more realistic and accurate 

model, at the expense of longer computation time. Since the optimization scheme might require a lot 

of simulations for each iteration, this can have a very large effect on computational time. Therefore, 

for this project the hydraulic timestep variable will have to balance an accurate hydraulic simulation, 

and a sufficiently short runtime for the optimization loop.  

3.4.2 Reporting timestep 
Reporting timestep is the interval between which output results are generated, it does not have any 

effect on the hydraulic simulation (Rossman et al., 2002). The reporting timestep does however 

determine the temporal resolution of the optimization model. For example: if the interval is one 

hour, only 1 pumps switch could be registered during that period. The reporting timestep must be 

greater than or equal to the hydraulic timestep and should also be an integer multiple of it to prevent 

the introduction of unintended intermediate timesteps. This is due to a every output reporting 

period will always require a new hydraulic timestep (Marini et al., 2023). 

3.4.3 Rule timestep 
Is the time step used to check for changes in system status caused by the activation of rule-based 

controls between hydraulic time steps (Rossman et al., 2002). By default, it is set to one-tenth of the 

hydraulic time step. If a hydraulic event is triggered (such as a maximum reservoir level), EPANET will 

insert an additional hydraulic solution step to recalculate the new status of system. The rule timestep 

can enable the use of a longer hydraulic timestep while still maintaining a sufficiently accurate 

hydraulic system.  

3.4.4 Interpolation interval timestep 
The trigger interval timestep is a “artificial” timestep introduced to lessen computation strain on the 

model. When constructing the trigger levels in the SCADA-system every value in between is 

established through linear interpolation. These interpolations are updated every minute. When 

recreating this in the simulation every interpolation needs to be defined as a new control rule. 

Updating the interpolation every minute is not feasible for the simulation since it would massively 

increase the amount of control rule which had to be added, and thus significantly increase 

computational times. Instead, the Interpolation interval timestep decides how often the 

interpolation should be performed. In the model the timestep was chosen to be 15 minutes, as a 

good balance between runtime and accuracy. Validation of this parameter choice is provided in the 

result section. Figure 3-4 illustrates the variables effect on the setpoint-curve. 



24 
 

 

 

Figure 3-4 Illustration of the effect Interpolation interval timestep has on the shape of the setpoint curve. 

3.5  Objective function 

3.5.1 Energy cost 
The driving force of this model will be to optimize the use of energy in a way which reduces the total 

cost. Minimizing energy cost can be divided into two parts: Reducing overall energy consumption and 

shifting consumption from high demand periods. It is important to note that these objectives can be 

conflicting, meaning that an optimal solution could increase the power consumption, if it is shifted to 

a lower demand period. The energy cost is calculated with by equation 3.1.  

𝐸 = ∑ ∑ 𝑃𝑖,𝑘γ𝑘

𝑛𝑝

𝑘=1

𝑇

𝑖=1

 (3.1) 

Where: 

𝐸 = Total energy cost over the time horizon 

𝑛𝑝 = Total number of pumps 

𝑇 = Total number of time steps. 

𝑃𝑖,𝑘 = Power consumption of pump k at time i 

𝛾𝑘 = Electricity tariff at time k 

 

3.5.2 Constraints 

Security of water supply  
As mentioned, one of the main aims of a reservoir is to increase reliability. Therefor it is important to 

always have a certain volume in case of an emergency such as pump failure, power outage, major 

leakage or any other major failure. Equation 3.2 defines the constraint which is based on securing a 

volume which can supply the High-pressure Zone for n hours, based on expected demand. The 



25 
 

dynamic nature of the constraint means that a greater volume will have to be kept before high 

consumption periods, e.g. Morning and evenings, in comparison to low consumption periods, e.g. 

during night.  

penSSV = ∑ δ𝑖

𝑇

𝑖=1

⋅ λ𝑆𝑆𝑉 ⋅ (∑ demand𝑖,𝑗

𝐻−1

𝑗=0

− volumei) (3.2) 

 

Where: 

penSSV = Weighted penalty for security of supply violation.  

𝐻 = “Emergency” duration in hours. 

𝛿𝑖  = Binary value ensuring penalty only activates when the rolling demand exceeds the stored 

volume. 

𝜆𝑆𝑆𝑉 = Penalty factor for security of water supply violation. 

demand𝑖,𝑗 = Current demand in timestep i in “lookahead horizon” j.  

Final reservoir level 
To retain a stable tank level between simulation horizons, the initial and final tank volume should 

ideally be minimized. Essentially, the stored volume inside the tank could be seen as potential 

energy. As such, unless the final reservoir level constraint is set, the optimal solution would converge 

towards solutions with lower final volumes. A penalty function is therefore needed to prevent this 

type of undesirable solution. Adding a hard constraint is undesirable since all solutions which obtain 

a final volume in the span between maximum and minimum, will at least be close to the feasible 

region. Instead, a penalty function based on the deviation from the final solution would be more 

suitable, as defined in Equation (3.3). This penalty is only applied when the final volume is lower than 

the initial volume. When the final volume is higher, no penalty is applied.  

 

pen𝐹𝐹𝐿 = 𝛿FFL ⋅ 𝜆𝐹𝐹𝐿 ⋅ (𝑉init − 𝑉final) (3.3) 

 

Where: 

penFFL = Weighted penalty for final reservoir level violation.  

𝑉init = Volume at initial timestep 

𝑉final = Volume at final timestep 

𝛿FFL = Binary value ensuring penalty only activates when final volume exceeds initial volume. 

𝜆𝐹𝐹𝐿 = Penalty factor for final reservoir level violation 

Maintenance cost 
It can be important to consider how optimization models affect the cost of maintenance. This refers 

to the additional wear caused by pumps operating in an inefficient manner. To simplify and 

concretize this, some type of surrogate measure is often used to account for maintenance (Mala-



26 
 

Jetmarova et al., 2017). In this thesis this surrogate measure will the number of times pumps turn 

on/off, referred to as pump switches. An allowable amount if pump switches will be set, then any 

more pump switch will result in a penalty factor, as can be seen in equation 3.4.  

 

𝒊𝒇 𝑆𝐴  >  𝑆ₜₕ  →  penPS = (𝑆𝐴  −  𝑆ₜₕ)  ⋅ 𝜆ₚₛ (3.4) 

 

Where: 

penPS = Weighted penalty for pump switch violations.  

𝑆𝐴   = Actual amount of pump switches 

𝑆ₜₕ = Threshold for acceptable pump switches. 

𝜆𝑃𝑆 = Penalty factor for exceeding the pump switch threshold  

Hydraulic simulation constraints  
The hydraulic feasibility of each solution is handled implicitly by hydraulic simulation (Rossman et al., 

2002). These constraints include acceptable ranges for: pressures in nodes, water levels in reservoirs, 

etc. These constraints are not explicitly expressed in the optimization scheme and are instead 

considered by registering warnings and crashes from each simulation run. If a solution contains a 

critical warning, the fitness of the solution will not be evaluated, and the solution will return a poor 

fitness value. If a non-critical warning is obtained, a penalty is added to the evaluated fitness 

function. The Constraint/penalty process can be seen in figure 3-5. 

 

 

Figure 3-5 Schematic overview of EPANET error/warning handling. 

 

 



27 
 

3.6  The Optimization algorithm 

3.6.1 Key-parameter encoding  
As an alternative using the 24-value setpoint curve string directly in the optimization algorithm, key 

parameter encoding is used. In the genotype each gene represents a meaningful coefficient which is 

not dependent on the rest of the genes (as was the case with the 24 values string). The genotype 

consists of 10 parameters which defines some key characteristic about the set-point curve, the rest 

of the values are interpolated to recreate a new string of 24 values (set-point curve). The 

encoding/decoding process can be summarized in figure 3-6. 

 

 

Figure 3-6 Schematic overview of the encoding–decoding process used in the genetic algorithm. 

 

The key-parameters contain information about how long each peak/dip are, and when in time each 

of these apexes occur. The genotype also contains information regarding the concave/convex nature 

of the curve in between these extreme points and the initial/final level. For simplicity and continuity, 

the endpoints always balance out, i.e. initial level = final level. The endpoints are thus defined by a 

single variable. A complete list of all genes in the genotype can be seen in table 3-1. 

 

Table 3-1 Description of variables in the key-parameter encoding scheme. 

Parameter 
Variable 

name 
Description 

Baseline Level L0 Defines the tank level at the start (t = 0) and end (t = 24) of the 24-
hour cycle. 

Peak Height HP Maximum level reached during the daily cycle. Represents the apex of 
the curve. 

Peak Timing TP Time of day when the peak level occurs. Controls the horizontal 
position of the peak. 

Peak Width WP Duration of the peak, how long the curve stays elevated. Influences 
steepness and curvature. 

Dip Timing TD Time of day when the lowest reservoir level (trough) occurs. 



28 
 

Dip Height HD Minimum level reached during the day. Typically, in the evening or 
night period. 

Dip Width WD Duration of the dip. Controls how sharp or extended the low-level 
period is. 

Rise Curvature CRV1 Controls the shape of the rise from L0 to HP. Affects steepness and 
concavity. 

Descent Curvature CRV2 Controls the shape of the fall from HP to HD. Refines the rounding of 
the descent. 

Recovery Curvature CRV3 Controls the shape of the recovery from HD to back to L0. Influences 
the tail of the curve. 

 

The key-parameter encoding offers a lightweight, yet powerful method to generate new solutions. It 

focuses on the key shapes of the set-point curve to work well in combination with the genetic 

algorithm. It uses a conscious simplification of the solution space to focus on feasible solutions. The 

main issue is that the encoding can be too simplified and thus unable to find the true optimal curve. 

For example, some demand pattern contains multiple peaks which a curve with a single peak/dip 

might be unable to handle optimally. A possible solution could be to introduce more parameters, but 

at the cost of a more complex solution space. In the end it comes down to a compromise between 

optimization potential and complexity. Figure 3-7 each variable can be seen in an actual curve. 

 

 

Figure 3-7 Visual representation of the key-parameters. 

 

 

 



29 
 

3.6.2 Pump trigger ranges variable  
To capture variations in pump trigger ranges an additional variable was added to the genotype to 

represent the overall “strictness” of the trigger thresholds. For simplicity, this was implemented as a 

single scaling variable, referred to as “pt_var”. The pump trigger ranges are initially defined based on 

the baseline control scheme and then uniformly scaled by this factor. Figure 3-8 illustrates the 

original trigger ranges (pt_var = 1) , while Figure 3-9 shows how the ranges are reduced when pt_var 

is set to 0.5. The differences between the figures illustrating how the pump trigger ranges become 

narrower around the set-point curve as the strictness parameter is reduced. 

 

 

Figure 3-8 Example of pump threshold ranges (pt_var = 1) 

 

 

Figure 3-9 Pump threshold ranges after scaling by pt_var = 0.5 



30 
 

This variable was primarily introduced to address the systematic deviation often observed between 

the setpoint curve and the actual reservoir level in the existing control system. In practice, the 

reservoir level does not perfectly follow the defined setpoint but instead oscillates around it. This 

discrepancy arises mainly from the relatively wide pump trigger ranges that define the allowable 

deviation from the setpoint before a pump is switched on or off. In figure 3-10 this deviations is 

shown by plotting the actual measured reservoir level and the corresponding setpoint curve during 

the day 2022-11-07. 

 

Figure 3-10 setpoint curve vs actual reservoir level, real-world data from 2022-11-07 

3.6.3 Mutation scheme  
The mutation operator utilized is a gene-wise probabilistic scheme. It includes a repair mechanism to 

ensure that all mutated individuals remain within feasible bounds (clipping). Since the initial 

population is generated from a near-optimal reference solution, the mutation scheme is intentionally 

biased toward local exploration. By employing parameter-specific mutation probabilities and step 

sizes, the approach offers fine-tuned control over search dynamics and enables specific adjustments 

based on insights from prior optimization runs. The mutation process is structured in three principal 

stages. Gene-Wise Probabilistic mutation, feasibility Clipping and peak-Dip Separation.  

Gene-Wise Probabilistic mutation 

First, each gene is assigned a mutation probability pᵢ. This probability is different from the global 

mutation parameter which determines if the mutation scheme should be triggered. If a given gene is 

selected for mutation, a uniformly distributed mutation-step 𝛿ᵢ ∈  [𝛥ᵢᵐⁱⁿ, 𝛥ᵢᵐᵃˣ] is sampled and 

added to the current gene value. The mutation can be seen in equation 3.5. 

 

𝑖𝑓 𝑟 <  𝑝ᵢ → 𝑥𝑛 =  𝑥𝑜  +  𝛿ᵢ (3.5)  

 

Where: 

𝑟 = Random value between 1 and 0.  



31 
 

𝑝ᵢ = Mutation probability.  

𝑥𝑛 = New gene value. 

𝑥𝑜 = Old gene value. 

𝛿ᵢ  = Mutation-step. 

𝛥ᵢᵐⁱⁿ = Lower limit of mutation range. 

𝛥ᵢᵐᵃˣ = Upper limit of mutation range. 

The mutation probabilities and step ranges are gene-specific and chosen based on the impact of each 

parameter. For instance, peak and dip timings may allow wider mutation ranges, while curvature 

parameters are adjusted more conservatively. 

Feasibility Clipping 
After mutation, each gene is clipped to its allowable domain to ensure physical feasibility. The 

bounds are defined based on operational limits of the reservoir (e.g., minimum and maximum water 

levels, valid time intervals, etc.). Clipping bounds can be found in table 3-2. 

 

Table 3-2 Clipping bound for key parameters 

Gene Min Max 

L0 79.65 81.1 

HP 79.65 81.1 

TP 0.0 24.0 

WP 0.0 24.0 

TD 0.0 24.0 

HD 79.65 81.1 

WD 0.0 24.0 

CRV1 -0.5 2.0 

CRV2 -0.5 0.5 

CRV3 -0.5 2.0 

 
 

Peak-Dip Separation 
A custom repair mechanism which enforces a minimum temporal separation between the peak and 

dip times. If the difference TD – TP violates the specified threshold (e.g. 1 hour), the dip time is 

adjusted forward or the peak time backward, depending on their location within the simulation 

horizon. This correction prevents the overlapping of peak and dip features, which could otherwise 

lead to infeasible curve structures. Figure 3-11 illustrates the peak-dip separation. 

 



32 
 

 

Figure 3-11 Visual representation of the Peak-Dip separation constraint 

3.6.4 Initialization Scheme 
The initialization approach employs a warm-start strategy in which all individuals are derived from a 

predefined base genotype, representing the current set-point curve used in the current control 

scheme. Injecting good solutions in the initial population has proven to be favorable in terms of 

search efficiency and reliability (Nicklow et al., 2010). Each individual in the initial population is 

generated by cloning this base solution and applying the existing mutation scheme to introduce 

localized variation. This ensures all initial candidates remain in the vicinity of a known feasible and 

operationally effective solution.  

3.6.5 Crossover Scheme  
The crossover strategy employs a block-wise recombination operator which is designed to preserve 

functional grouping within the genotype. Traditional crossover operators in genetic algorithms do not 

always retain the beneficial traits of the parent individuals, which can lead to lower-quality offspring 

and reduce the overall performance of the algorithm (Da Silva Brito et al., 2023). When crossover is 

applied, one of several predefined blocks, covering time-location parameters, height values, or 

curvature descriptors is selected and exchanged between parents. The likelihood of each block being 

chosen is governed by a weighting variable. Occasionally, a full two-point crossover is used to 

introduce greater diversity. The predefined block of the crossover scheme can be seen in figure 3-12.  

 

 

Figure 3-12 Visual representation of the block-based crossover scheme. 

 



33 
 

This approach helps keep related features, like the shape and timing of peaks or dips intact during 

crossover, while still allowing new variation to be introduced when needed. It works well for 

genotypes where some parameters depend on each other, since randomly mixing genes could break 

important combinations and lead to worse solutions. 

3.6.6 Elitism Strategy  
To ensure that the best solution found so far is not lost between generations, the algorithm 

incorporates an elitism mechanism. At the end of each generation, the current best individual is 

explicitly preserved and reintroduced into the next population without modification. This guarantees 

that the most fit solution is always retained, providing a safeguard against regression in solution 

quality. 

3.6.7 Selection strategy   
The genetic algorithm employs tournament selection, which was explained in the literature section. 

The tournament selection method is particularly effective for problems where the objective function 

includes multiple penalty/constraint terms since it relies on relative comparisons rather than global 

fitness scaling. 

3.6.8 Parallelization  
To significantly speed up the optimization loop, parallelization was implemented. The 

implementation is based on “distributed fitness evaluation” which is generally considered the most 

standard approach for parallelization in the context of GAs (Sivanandam & Deepa, 2008). More 

specifically a “Master-Slave” configuration is used, which uses a single population where the 

evaluation of solutions is performed in parallel by the “slave” processes. The “master” process is 

essentially responsible for the main GA loop, sending out each individual to available “slaves” and 

collecting the results and at the end of each iteration. The “master” process is also responsible for 

updating the population for each new generation, performing the mutations and crossover 

operation. In figure 3-13 the general structure of the “Master-Slave” configuration can be seen.  

 

 

Figure 3-13 Schematic overview of the parallel evaluation process using a “master-slave” method. 

 



34 
 

3.6.9 Hyper-parameter strategy 
A heuristic/"trial and error" hyperparameter tuning process was used to configure the genetic 

algorithm, remembering the "no free lunch theorem", there is no universally optimal set of 

parameters that works across different problems and system setups. The tuning was guided by 

structured experimentation and domain-specific insight. The goal was to identify a balance between 

exploration and exploitation in the algorithm, while maintaining reasonable run-times.  

The most influential parameters were identified based on the shapes of the resulting setpoint curves. 

These were subsequently fine-tuned to ensure that various local optima and regions of the solution 

space were thoroughly explored. 

3.7   Scenario evaluations  
To validate the optimization algorithm, different scenarios were evaluated to confirm its function and 

validity. These scenarios are based on hydraulic models described in Section 3.2. 

3.7.1 NET-1  

Parallelization test 
In this test the effect of parallelization was tested on the optimization algorithm using the NET-1 

hydraulic model. Due to the available hardware, 6 processes where available to be run in parallel.  

Net-1 Simple optimization scenario 
In this scenario a simple artificial optimization scenario is introduced to provide meaningful insight in 

how the algorithm operates. The optimization algorithm can essentially be described as a “grey box” 

model. This mean that it incorporates elements from white-box models, which are fully based on 

known physical laws and equations. But also contains elements of a black-box model, which are 

completely data driven. For a more complex hydraulic scenario, with different constraints, the 

reasoning of the model can be quite hard to follow. This scenario aims to use fewer objectives to 

provide a better understanding of how the algorithm operates.  

In this scenario a special tariff period is introduced to the NET-1 hydraulic scenario. These tariff 

periods consist of 3 different periods: high, medium and low. Also, a general initial set-point curve 

was used as a starting point for the optimization algorithm. The tariff periods and an the initial 

(unoptimized) setpoint-curve can be seen in figure 3-14.  

 

 

Figure 3-14 Tariff periods and initial (unoptimized) setpoint curve 



35 
 

 

It can be worth noting that this tariff scheme is not grounded in any actual data and thus holds no 

actual real-world validity. It is intentionally constructed so that the optimization scheme must make 

substantial changes to the initial setpoint-curve. providing clearer insight into its behaviour. 

 

3.7.2 HPZ-G 

Timestep Sensitivity Analysis 
In order to evaluate how different timestep setting affect runtime and accuracy, a simple sensitivity 

analysis is done. The goal is to identify a suitable balance between efficiency and quality, by 

evaluating each timestep individually. As mentioned, the rule timestep cannot be explicitly set, and is 

instead calculated from the hydraulic timestep. It is therefore not included in the sensitivity analysis. 

A high-resolution baseline scenario was established using low values for all the relevant timesteps. 

This baseline scenario was meant to represent a high accuracy simulation and served as a reference 

point for all the comparisons. The accuracy is determined by the energy cost calculation. The values 

used for the baseline scenario can be seen in table 3-3.  

 

Table 3-3 Timestep variables for "baseline scenario" 

Timestep: Hydraulic Reporting Interpolation 

Value: 5 10 10 

 

Each timestep variable was then increased individually, enabling evaluation of how each variable 

affected simulation efficiency and deviations in simulation result. Certain timestep variables are 

dependent on others and cannot be changed completely independently. For example, the hyd