i

UNIVERSITY OF NAIROBI

FACULTY OF ENGINEERING

DEPARTMENT OF ELECTRICAL AND INFORMATION ENGINEERING

PROJECT TITLEOPTIMAL PUMP SCHEDULING

PROJECT INDEX033

BYNYANGARESI BRIAN NYACHIO

F17/36896/2010

SUPERVISORMR. AHMED SAYYID

EXAMINERPROFESSOR ELIJAH MWANGI

PROJECT REPORT SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTFOR THE AWARD OF THE DEGREE OF:

BACHELOR OF SCIENCE IN ELECTRICAL AND ELECTRONIC ENGINEERING OF THEUNIVERSITY OF NAIROBI, 2015

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DECLARATION OF ORIGINALITY

NAME OF STUDENT: NYANGARESI BRIAN NYACHIO

REGISTRATION NUMBER: F17/36896/2010

COLLEGE: Architecture and Engineering

FACULTY/SCHOOL/INSTITUTE: Engineering

DEPARTMENT: Electrical and Information Engineering

COURSE NAME: Bachelor of Science in Electrical and Electronic Engineering

TITLE OF WORK: OPTIMAL PUMP SCHEDULING

1. I understand what plagiarism is and I am aware of the university policy in this regard.

2. I declare that this final year project report is my original work and has not been

Submitted elsewhere for examination, award of a degree or publication. Where other

people’s work or my own work has been used, this has properly been acknowledged and

referenced in accordance with the University of Nairobi’s requirements.

3. I have not sought or used the services of any professional agencies to produce this work.

4. I have not allowed, and shall not allow anyone to copy my work with the intention of

passing it off as his/her own work.

5. I understand that any false claim in respect of this work shall result in disciplinary action,

in accordance with University Anti-plagiarism policy.

Signature

………………………………………………………………………………………………………………………………………

Date

………………………………………………………………………………………………………………………………………

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DEDICATIONTo my dear mother Mellen Kerubo who religiously dedicated her efforts financially, emotionally

and physically to ensure that I see this day of my academic life. To the almighty God, that killed

the spirit of despair in me and guided me through to this day.

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ACKNOWLEDGEMENTI would like to acknowledge my supervisor who sacrificed his time to guide me through this

project and ensure I succeed. I also would like to acknowledge the other lecturers who were there

for consultation and to offer guidance. I would also like to acknowledge my friends who we have

been together in this journey that has had all the ingredients of life.

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LIST OF ABBREVIATIONS

PSO Particle Swarm Optimization

MD Maximum Demand

POET Performance, Operation, Equipment and Technology

LS Load Shifting

EE Energy Efficiency

GA Genetic Algorithm

VSD Variable Speed Drive

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LIST OF FIGURESFigure 3. 1 Head Curve ...............................................................................................................................12Figure 3. 2 Efficiency Curve .......................................................................................................................13Figure 3.3 multi-level setup ........................................................................................................................14Figure 3.4 crossover ....................................................................................................................................17Figure 3.5 mutation .....................................................................................................................................18Figure 3.6 Genetic algorithm process. ........................................................................................................21

Figure 4.1 power consumption....................................................................................................................30Figure 4.2 head capacity relation ................................................................................................................31Figure 4.3 Pump activation time .................................................................................................................34Figure 4.4 reservoir levels...........................................................................................................................34Figure 4.5 energy cost over capacity...........................................................................................................36Figure 4.6 low tariff pump activation..........................................................................................................37Figure 4.7 low tariff reservoir size ..............................................................................................................38

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LIST OF TABLESTable 2. 1 Tariffs...........................................................................................................................................5

viii

ABSTRACTThe objective of this project is to optimally schedule pumps to ensure that while in operation the

operational efficiency is high but at the same time the cost of running the pump is kept on the

minimum.

This project dwells on pumping systems especially water supply pumping systems. Society

keeps growing each day and this, therefore, means that demand for basic commodities is on the

increase. Water is a basic need for human life and is of great demand. To meet the given

demands water supply systems must be expanded in relation to demand. Pump scheduling

optimization has therefore become necessary. The main aim of pump scheduling is to schedule

the operation of a given number of pumps in such a way that system constrains and boundary

conditions are satisfied while operation cost is minimized. Most important costs associated with

pump operations are electrical and maintenance cost. This adds up to the total cost of running the

pump system thus making it costly altogether. Ways have to be found on how best these

problems have to be overcome without compromise the operation results at the end. Various

techniques are applied, some manually some automated. All this cuts down to what is the most

suitable approach.

To efficiently schedule pumps different approaches have been used before. These include linear

programming, non linear programming, multi objective approach and genetic algorithm

optimization [5]. However, in this project we approach the problem using particle swarm

optimization. This approach will be expounded further in the following chapters. The report

approaches the issue by considering water supply systems which are the most common systems

that heavily rely on pumping systems.

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CONTENTSDECLARATION OF ORIGINALITY........................................................................................... ii

Dedication...................................................................................................................................... iii

Acknowledgement ......................................................................................................................... iv

List of abbreviations ........................................................................................................................v

List of figures................................................................................................................................. vi

List of tables ................................................................................................................................. vii

ABSTRACT ................................................................................................................................ viii

CHAPTER 1 ....................................................................................................................................1

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

CHAPTER 2 ....................................................................................................................................3

LITERATURE REVIEW ................................................................................................................3

2.1 SYSTEM OPTIMIZATION ......................................................................................................................3

2.2 ENERGY AND LOAD MANAGEMENT....................................................................................................3

2.3 TARRIF STRUCTURES ...........................................................................................................................4

2.4 ENERGY EFFCIENCY ANALYSIS .............................................................................................................5

2.5 PUMPING SYSTEMS PHYSICAL COORDINATION..................................................................................6

2.6 PUMPING SYSTEM TIME COORDINATION...........................................................................................6

2.7 OPTIMIZATION APPROACH .................................................................................................................6

2.7 POWER CONSUMPTION FUNCTION....................................................................................................7

2.8 choice of pump drive...........................................................................................................................8

CHAPTER 3 ....................................................................................................................................9

Supply system..................................................................................................................................9

3.1 WATER SUPPLY SYSTEM......................................................................................................................9

3.1.1 WATER SOURCE............................................................................................................................9

3.1.2 HOLDING TANKS...........................................................................................................................9

3.1.3 PUMP SYSTEMS............................................................................................................................9

3.1.4 PIPE NETWORKS ...........................................................................................................................9

3.1.5 PUMPING SYSTEMS OPERATION................................................................................................10

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3.1.6 PUMP SYSTEM HEAD PARAMETERS...........................................................................................11

3.1.7 PUMP PERFORMANCE CURVES..................................................................................................12

3.1.8 MULTI LEVEL PUMPING SYSTEM................................................................................................13

3.2 APPROACHES USED IN SCHEDULING PUMP OPTIMIZATION ............................................................14

3.2.1 LINEAR PROGRAMMING ............................................................................................................15

3.2.2 MULTI-OBJECTIVE APPROACH....................................................................................................15

3.2.3 GENETIC ALGORITHM APPROACH..............................................................................................15

3.2.3.1 INITIALIZATION....................................................................................................................16

3.2.3.2 SELECTION...........................................................................................................................16

3.2.3.3 CROSSOVER .........................................................................................................................17

3.2.3.4 MUTATION ..........................................................................................................................17

3.2.3.5 GENETIC ALGORITHM PARAMETERS AND DEFINITIONS.....................................................18

3.2.3.6 STOPPING CRITERIA ............................................................................................................20

3.2.4 PARTICLE SWARM OPTIMIZATION .............................................................................................21

3.2.4.1 PSO PROCESS.......................................................................................................................22

3.2.4.2 BENEFITS OF PSO.................................................................................................................23

3.2.4.3 CHALLENGES OF PSO...........................................................................................................23

CHAPTER 4 ..................................................................................................................................25

PROBLEM FORMULATION ......................................................................................................25

4.1 FUNDAMENTAL OF PSO ....................................................................................................................25

4.2 MODEL SELECTION AND TESTING .....................................................................................................28

4.3 OPTIMIZATION ALGORITHM .............................................................................................................28

4.4 SIMULATION RESULTS AND DISCUSSION..........................................................................................33

4.4.1 HIGH DEMAND TIME..................................................................................................................35

4.4.2 LOW DEMAND TIME...................................................................................................................36

4.4.3 RESERVOIR LIMITS......................................................................................................................37

chapter 5.........................................................................................................................................39

CONCLUSION..............................................................................................................................39

5.1 RECOMMENDATION..........................................................................................................................40

REFERENCE ................................................................................................................................41

APPENDIX....................................................................................................................................43

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1

CHAPTER 1

INTRODUCTION

Areas with good access to water tend to have large human population. However, not everybody

can live next to a water source. This explains why water supply systems have to be built to serve

all, irrespective of how far away they are from the water source. A water supply system is the

infrastructure that is put in place to collect, store and distribute water within a given area. Supply

systems basically comprise of storage tanks, piping systems and pumps. Water supply systems

vary in sizes depending on the demand they have to meet. A good water supply system must

meet the water demand of a given population. This then guides us on how best to build systems

and optimize them to operate in the best way possible at the least cost.

There are various problems that are encountered in the process of trying to meet water demands.

Today, human population has grown almost in ten folds. Authorities charged with ensuring

proper water supplies are encountering major challenges. A larger population means expanding

water supply systems to meet demand. However, to expand a supply systems means expenses

have to be incurred. Various expenses come with expansions. As mentioned earlier, these include

electrical and maintenance cost. The main source of energy in most developing worlds is

electricity. However the supply of electrical energy is incapable of matching the demand. This

makes electrical energy very costly. This cost is transmitted to the water supply system which

heavily relies on electricity to power up the supply pumps. This cost is even worse for poorly

scheduled pumps. Energy charges in most areas vary from time to time depending on demand.

This makes it hard for supply systems to ‘tame’ the energy cost that the energy production and

supply sector comes up with.

Maintenance cost comes about due to the day to day running of the water supply systems.

Pumping systems involve many pump networks which require many pumps to move fluids from

one area to another. The number of times a pump runs determines how fast it will wear out. This

therefore brings about expenses that come about when replacing faulty or worn out pumps.

Pumps come in different sizes and with different heads. This also dictates the expenses incurred.

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Through all these aspects considered, this report puts all of them into consideration and then

identifies the best way through which pumps can be optimally scheduled while at the same time

minimizing the costs that come with pump operation and, largely, with operating water supply

systems.

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CHAPTER 2

LITERATURE REVIEW

2.1 SYSTEM OPTIMIZATIONThis report focuses on the analysis of pump operations, improvement based on performance,

operation, equipment and technology. This optimal approach breaks down the pump

optimization analysis into two issues: energy efficiency and load shifting. Energy is a key factor

when dealing with energy dependant systems. Energy efficiency aims to improve energy use and

minimize on cost. Production of energy is costly [10]. To add onto that we have transmission and

distribution cost. Cumulatively, all these add up to energy cost. This cost trickles down to the

energy consumer. This therefore demands that measures have to be put in place to counter the

cost and at best minimize unnecessary energy use and thus reduce energy wastage. Load shifting

involves systematic selection of load based on necessity with the aim of reducing loading o f the

pumping system during peak times. Time of day determines the kind of load that is in demand of

energy. Big loads within a given time may make energy costly. Therefore load balance should be

carried out to ensure that the loads are distributed in a balanced manner to minimize demand in a

given period [11].

Other measures are also undertaken to solve the energy problem. Less expensive, fast and

cleaner initiatives have to be undertaken. Some can be done on a large scale while others can be

system based. To carry out complete system overhaul can be costly. However, system

modification can achieve the required objective. This goes a long way to achieve reduction in the

electricity demand and cost. In this research our operation efficiency is determined based on how

best the cost of the system can be reduced. The root aim is to ensure that the operation cost is

kept on a low while still achieving the optimization objectives. To achieve these objectives we

use binary and continuous solutions simultaneously. This explains why we choose to use particle

swarm optimization.

2.2 ENERGY AND LOAD MANAGEMENTMost systems are energy dependent. To attain high efficiency in a system, energy balance has to

be carried out. As mentioned earlier, energy demand in modern day surpasses the energy

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available for supply. This therefore calls for an efficient use of energy to minimize on cost and

reduce wastage [9]. There is a heavy reliance on electrical energy. However, other forms of

energy that are cheaper, clean and efficient can also be exploited. Such form of energy is the

solar energy. Solar panels can be used to harness solar energy which then can be fed to the

energy supply system. Areas with adequate sunlight can substitute electrical energy use during

sunshine peak when the amount of solar radiation is high.

In load management the focus is shifted to the system load. Cost reduction options are now based

on the load that is consuming energy. Ways of reducing large loads within a given period are

considered. Loads that can operate comfortably within other periods are shifted to those less

loaded times. This is what is called load shifting. Load shifting is also a measure of ensuring

there is reduced cost of operation. A control system is used to ensure that the maximum loading

occurs during off peak charging of electrical energy and when there is a low demand of power.

Load shifting systems are used to achieve this. Therefore proper analysis has to be carried out to

ensure that proper shifting of load is carried out without affecting the efficiency of a given

system.

2.3 TARRIF STRUCTURESTariff is the billing structure used to charge energy consumed by a certain entity [6]. Various

countries have different tariffs based on the amount of energy available and the kind of energy

demand. High energy demand in a region with little energy supply has a high charging rate.

Energy consumption is measured in kilowatt hour (KWh). There is a set price value for 1KWh.

However energy charges vary depending on the time of day. Few countries have fixed tariffs.

Energy is costly during high peak demand and less mostly during off peak demand. Off peak is

the period when the power demand is very low [6].

Based on this energy structure most water supply systems ensure that they load the system to the

maximum during low costing periods and limit the amount of load during peak charging periods.

This is also a measure used to ensure low cost of operation. During high cost periods of energy

alternate energy sources, as those mentioned previously, are used. These include energy from

wind harnessed using wind turbines and solar energy harnessed using solar panels.

5

Charge structures are set in a way that we have a maximum demand charge which is the highest

cost of electricity in a given period. Charges are capped at this limit. Notified maximum demand

is the value set that a customer should not exceed. Different customers have different notified

maximum demand depending on their energy use tendency. For supply systems, such as water

supply systems, their notified demand tends to be higher. The tariff price ranges used in this

report are as shown in table 3.3. This is from a general value basis based on the Kenyan tariff.[7]

Table 2. 1 Tariffs

Period Cost

Off-peak (0:00 to 6:00 and 22:00 to 24:00)

High Demand 10.45Ksh/kWh

Low Demand 8.50 Ksh /kWh

Standard (6:00 to 7:00 and 10:00 to 18:00)

High Demand 12.25 Ksh /kWh

Low Demand 11.50Ksh /kWh

Peak (7:00 to 10:00 and 18:00 to 22:00)

High demand 14.00 Ksh /kWh

Low Demand 13.25Ksh /kWh

Maximum Demand Charge 66.50 Ksh /kVA

2.4 ENERGY EFFCIENCY ANALYSISEnergy efficiency analysis is done in four main approaches: system performance, operation,

equipment and technology used [10]. For a given energy system the performance efficiency is

based on external factors such as production, technical indicators, cost, energy sources and many

other factors. The operation efficiency of an energy system considers coordination between

human and the different system components that make up the system. Equipment efficiency is a

measure of the energy output of the individual systems in an energy system compared to the

design specifications of the system. This looks at whether the requirements achieve the set

expectations in an energy system. Individual equipment have specific set standards that they are

expected to operate within. For technological factors, an energy system is analyzed based on how

6

efficient energy conversion is, the processing steps, energy transmission and how effective is the

energy supplied used.

2.5 PUMPING SYSTEMS PHYSICAL COORDINATIONIn a pumping system various requirements are set. These guide the operation of a system and

ensure that it is within the set guidelines. The equipment have to be matched to specific

operation guidelines that are set. This is the physical coordination. To achieve high efficiency

and low cost of operation equipment matching should be done to an acceptable level [9]. Poor

matching leads to low efficiency and subsequent high cost. This, therefore, calls for optimal

selection of equipment to be used in a pumping system. In depth research about equipment has to

be carried out and proper knowledge about equipment use has to be obtained. This will ensure a

flawless system setup and work towards achieving system efficiency.

If different operation conditions are well simulated, identification and selection of the most

economic combination of equipment is simplified. Operational energy cost is a major contributor

to the long term cost of a given pump life cycle. Nearly 90% of the cost of in the pump’s life

cycle is heavily caused by the energy the pump consumes [25]. Thus through proper pump

selection the cost can be reduced by 20%. For proper pump operations the performance

characteristics of a given pump must always be in line with its intended purpose. The correct

pump selection is therefore the main step to achieving the required pump efficiency.

Optimization algorithm and techniques are then employed to identify the best pump selection.

2.6 PUMPING SYSTEM TIME COORDINATIONTime coordination is a focus on the optimal control of pump operations in a pumping system.

Initially most pumps relied on valves to control the output of the pump. This is still used because

it’s a cheaper way of controlling pump systems and also considered simple in implementation.

However valve control of pumps leads to poor energy efficiency [9]. This beats the purpose of

carrying out pump optimization to achieve pump operation efficiency in pumping systems.

2.7 OPTIMIZATION APPROACHThe first hypothesis considered is to develop a complete pump efficiency scheme. We consider

the operation factors and generally the factors mentioned previously which are the performance,

operation, equipment and technology [10]. The second hypothesis considered is that to minimize

7

the operation cost, energy efficiency and load shifting can be combined in a balanced way when

selecting and operating water pumps.

The approach taken in this research focuses on physical and time coordination of the system

operations. To attain pumping system operation efficiency approach consists of three stages so as

to simplify the problem.

First an optimal pump selection model is developed. This model is used to select the optimal

pump capacities of a given pumping system with the aim of cutting down on operation cost and

energy cost. To achieve this, energy efficiency and load shifting contributions have to be

balanced.

Secondly we formulate and test a flexible open loop pump control starting with minimizing the

net savings from energy efficiency and load shifting contributions using a variable speed drive

based control. This proposed strategy is designed to cater for any occurring system changes and

adjust itself to ensure minimal operation cost. However, for this report we consider optimal

pump capacity selection approach. This is delved into in details in subsequent chapters. Optimal

pump scheduling is still achieved with whatever approach used.

2.7 POWER CONSUMPTION FUNCTIONTo minimize operation energy consumption of pumps in use pump power consumption under

different scenarios is analyzed and determined [4]. The relationship between the optimization

variables and pump power consumption is formulated.

The first relationship considered is the pump capacity and the pump power consumption. This is

the capacity-power function. It is used in the optimal pump selection model and estimates the

pump power consumption for different pump capacities. Another relationship considered is the

pump flow rate and the pump power consumption. This is the flow-power function. It is used in

the optimal control and computes pump power consumption for different flow rate settings of a

variable speed drive controlled pump.

Power prediction functions should not be complex. Complex optimization algorithms might

become unsolvable. Pump characteristics and system characteristics can be accurately estimated

by quadratic equation. Power prediction functions for fixed speed pumps can be obtained from

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hydraulic equation. This input power function for fixed speed pumps can be used to formulate

the capacity power function.

2.8 CHOICE OF PUMP DRIVEWhen using variable speed drives for load shifting in optimal control various difficulties are

encountered. A centrifugal pump can only run above a given minimum speed with which the

motor rotates. If not, the water swirls within the pump and little or no water is pumped [12]. The

speed of a variable speed drive (VSD) can be adjusted from zero to maximum. Operating a pump

below the required minimum speed causes it to overheat and wastes energy. The VSD has a

speed adjustment of 25% to 50% of the maximum motor rotating speed. This limited range limits

the level of load shifting.

In light of this problem the controller is required to shut down a pump when the operation isbelow the minimum rotational speed. This therefore requires an on/off control to be part of aVSD operation.

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CHAPTER 3

SUPPLY SYSTEM

3.1 WATER SUPPLY SYSTEMWater supply systems are a combination of different parts. All these are necessary in ensuring

that the objectives of a supply system are achieved. There are four main parts that make up a

water system.

3.1.1 WATER SOURCEFor a water supply system to be setup there has to be an adequate water source to supply it. Most

water supply systems rely on water from distribution reservoirs such as dams, water treatment

plants and other reservoirs. These reservoirs must have enough water to supply the supply

system continuously with water.

3.1.2 HOLDING TANKSWater from reservoirs is collected and stored in storage tanks. These tanks provide water for

distribution to various areas where water is required during peak times when water required is

more than that pumped. Most storage tanks are artificially built. During low demand seasons

pumped water is stored in the holding tanks.[3]

3.1.3 PUMP SYSTEMSMost water supply systems require pumps to push water over long distances where gravity alone

cannot work. There are different types of pumps but the most commonly used in water supply

systems is the centrifugal pump. Pumps come in different sizes depending on the amount of work

they are required to do. Proper pumps have to be fitted in water supply systems to ensure

efficient supply.

3.1.4 PIPE NETWORKSThis is a key installation in supply systems. There are different levels of pipe networks from

primary to service connection pipes. The primary distribution pipe networks carry water from the

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supply system. The distribution networks, carry water from the main channel to given regions.

Finally the service connection pipes take the water to various consumer points.

3.1.5 PUMPING SYSTEMS OPERATIONPumps are necessary in attaining the necessary head required and to overcome resistance

encountered during the flow of water. Very few areas can have water supply systems that solely

rely on gravitational force to move water from one point to another. Areas where water flows

from a region on a lower ground to a region on higher ground require heavy pumps to overcome

the resistance.[4]

Pump operations depend heavily on how a water supply system is set up. Pipes have to be set up

properly and should be the right size. Storage tanks must also be well placed. All these are

therefore carefully considered when installing water pumps to ensure they work properly and

efficiently.

When installing water pumps, one has to take into consideration the pump’s head capacity

because this determines the kind of flow the pump will provide. The system’s head has to be

considered too. The head versus discharge curve of pump are plotted on the same scale with

system head curve to determine the head losses that come with the flow such as frictional losses.

Through the total flow ad minor losses the running behavior of the pump can be determined. The

observations obtained can then be used to analyze the kind of head values the pump is capable of

providing.

Pumps in a water distribution pumping system can be installed in parallel or series. These pumps

can be of the same type or different. Pumps can also be installed both in series and parallel. This

therefore demands that the total behavior of the pumps be obtained. The combined system head

and flow values can be obtained through superimposition of the pump curve and combined total

value of the system flow curve.

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3.1.6 PUMP SYSTEM HEAD PARAMETERSPumps have four major head parameters. These are: static suction lift, static discharge head, total

discharge head and total dynamic head. The values of these parameters are used to study pump

systems and operations such as the condition and operation of the pump and the inlet and outlet

characteristics of the pump. This then helps in making the right choice on the kind of pump that

should be installed for use in pumping systems. [4]

Static suction lift is the elevation difference between water level in source tank and centerline

axis level of the pump. If the elevation of water level in source tank is higher than pump, the

static suction lift is positive. If the elevation of water level in source tank is lower than pump,

then water in source tank flow by the pump vacuum effect and static suction lift is negative.

The elevation difference between water level in discharge tank and centerline axis level of the

pump is static discharge head. Summation of both static suction lift and static discharge head is

total static head which is the elevation difference of source and discharge tanks directly.

If the friction losses and minor losses are added to total static head, then total dynamic head or

total head is achieved. Total head is determined as below:

HP = ∆Z + hL ( 3.1)

where:

Hp is total pump head

∆Z is the total static head

HL is total friction and minor losses

The flow that is obtained from a running pump has a direct relationship to its head capacity. This

information is provided by the pump manufacturers. Figure 3.1 shows the operation point to be

the intersection between pump curve and system head curve. Equilibrium between pump head

and the total system head is attained at the operation point. [2]

12

Figure 3. 1 Head Curve [2]

3.1.7 PUMP PERFORMANCE CURVESPump head capacity, power capacity and efficiency curves are graphically represented on pump

performance curves. During pump manufacturing the performance cure of each pump is plotted

based on the test results obtained. This works as the identity of the pump that has been

manufactured. Pump performance curves are therefore important in choosing ideal pumps for a

given system.

The head capacity curve is the basic performance curve which is useful in explaining the

relationship between pump discharge. For a given head value only one discharge value should be

obtained from the performance curve. More than one discharge value for a specific head the

pump shows instability during running by providing different flows at the head.

Efficiency of a pump provides information regarding to energy consumption of a given pump.

Power curves can be constructed by using power delivered to the pump in order to provide

related flow rates. Power consumption of a given pump can be obtained using the equations

given below:

13

= . . .ƞ (3.2)

Where:

P: pump power (watts)

ρ : fluid density (kg/m3)

g : acceleration due to gravity

Qp : pump flow rate (m2/s)

Hp : pump head (m)

Ƞ : efficiency

Qp and Hp are values that are directly obtained from pump head curve. Efficiency ƞ is obtained

using pump efficiency curves. The pump performance curve is shown in figure 3.2

Figure 3.2 Efficiency Curve [2]

3.1.8 MULTI LEVEL PUMPING SYSTEMIn this research optimal pump selection is carried out for multi-level pumping system. Figure

3.3 shows an example of a multi-level pump setup

14

Figure 3.3 multi-level setup [13]

Classification of different pump levels is based on the pump arrangement. Each level has a

cluster of pumps. This can comprise of one or more interconnected pumps that have a common

input and output. In some cases multi reservoirs can be at each level

3.2 APPROACHES USED IN SCHEDULING PUMP OPTIMIZATIONOptimization, specifically pump scheduling optimization, can be achieved through various

techniques. Various parameters are considered when choosing the most suitable optimization

technique. This is because not all techniques can achieve the optimum levels expected in a

certain exercise. Different projects have various factors they optimize, such as the amount of

power consumed, the maintenance cost being kept low or even operation cost.

15

3.2.1 LINEAR PROGRAMMINGThis is one of the most commonly used approaches in optimal pump scheduling. The constants in

question and the variables are carefully considered and if there is linearity, then a linear equation

is formed which is then used in programming to obtain the optimum results expected. Most times

cost of operation or tariffs are optimized using linear programming. However this is not the best

of methods when wants the best results in optimizing pump operations.

3.2.2 MULTI-OBJECTIVE APPROACHThis is a combination of different approaches to obtain the best results. Most algorithms focus on

a single objective, say, minimize the cost of pumping. Multiple objectives and alternative

representations are important factors when choosing the type of optimization algorithms to use in

water distribution systems. Currently most problems are solved by bi-objective approach, where

the objectives are: minimize operation cost of pumping and, say, reduce number of switches.

More research on this approach has led to an advanced multi-objective algorithm [16].

3.2.3 GENETIC ALGORITHM APPROACHGenetic algorithms are adaptive algorithms used to obtain optimum solution for an optimization

problem. Canonical genetic algorithm is characterized by binary representation of specific

solutions, crossover and mutation operators, and a proportionally balanced selection guideline.

Genetic algorithm approach tries to imitate the biological genetic processes [5]. It is a successful

method for optimization. This approach works with set of possible solutions, simultaneously,

called population. It repeatedly modifies the population of individual solutions. For every step

the GA picks individuals randomly from a given population to be parents. These parents are used

to produce children for the next generation. Successively after a number of tries the population

evolves to an optimal solution. GA can be used to solve a variety of optimization problems that

cannot be successfully solved using the standard optimization techniques. Members of the

population are strings or chromosomes, which are originally binary representations of solution

vectors. Genetic algorithm selects subsets of solutions from parents then combines them to

produce offspring (children). The guidelines used in combining the parents to yield children are

based on the genetic theory of crossover. This involves interchanging solution of a given set of

16

values of a given set of variables, together with operations such as random value changes (a

process called mutations).

Children produced by the mating of parents are then available to be chosen as parents of the next

generation, after passing certain set standards. Parents are chosen randomly based on a biased

scheme which can be carried out in parallel, in some situations, over separate Sub-populations

whose best choices are occasionally shared or exchanged. Genetic algorithm is used as described

below:

3.2.3.1 INITIALIZATIONIn this stage, coding structure is chosen. This is the format that will be applied all through.

Coding for a solution, which is called chromosome in Genetic Algorithm, is described as a string

of symbols from, say {0, 1}. The chromosome components are then labeled as genes. The

number of bits used to identify parameters, are problem dependent. Assume a population m with

solutions xi, where i=1, 2, 3 …, m, is a string of symbols {0, 1} of length l. The initial population

of m solutions is selected completely at random, with each bit of each solution having a 50%

chance of taking the value 0.[5]

3.2.3.2 SELECTIONProportional selection is applied in genetic algorithm. This is the second step in using genetic

algorithm where we determine the population of the next generation the by taking n independent

random experiments n independent random experiments. The probability th*-at xi is selected

from x1, x2, x3 ... xm , to be a member of the next generation is obtained by:

P {xi is selected} =( )∑ ( ) > 0 (3.3))

This process used is viewed as a roulette wheel where each member of the population is

represented by a section proportional to the member’s fitness. A spin of the wheel is used to

select, ultimately ending up eliminating the least fit members.

17

3.2.3.3 CROSSOVERThe next step is called the crossover step. In this process two parent chromosomes are used to

produce a new child by combining the genetic information from the parents [5]. GA uses the one

point crossover method as will be illustrated in a diagram of figure 3.4. Here we consider a

chromosome of a length l. then we pick a random number k between 1 and l is which is first

generated. The first child chromosome is obtained by appending the last l−k elements of the first

parent chromosome to the first k elements of the second parent chromosome. The second child

chromosome is formed by appending the last l−k elements of the second parent chromosome to

the first k elements of the first parent chromosome. Thus probability for crossover is from 0.6 to

0.95.

Figure 3.4 crossover

3.2.3.4 MUTATIONMutation is another step used in genetic algorithm. However, it is normally considered as a

background operator. It works independently on each individual. To mutate we generate a

random number v between 1 and l and then make a random change in the vth element of the

18

string with probability pm ϵ(0, 1). Typically, bit mutation probability ranges from 0.001 to 0.01.

Genetic algorithm has the following unique features:

They operate on coding of the parameter sets instead of parameters themselves

They search with a population of points, not a single point

They use the objective function information directly, rather than the derivatives or

other auxiliary knowledge, to find maxima

They process information using probabilistic transition rules, rather than deterministic

rules.

These features make Genetic Algorithm flexible to computation, easy to implement and a

powerful global optimization technique. Figure 3.5 shows a representation of how mutation

occurs.

Figure 3.5 mutation

3.2.3.5 GENETIC ALGORITHM PARAMETERS AND DEFINITIONSWhen using the Genetic Algorithm approach to solve an optimization problem there are unique

terms and parameters that are used to ensure that the required results are obtained as expected.

The algorithm flow must be correct and each parameter must be included and well defined. The

parameters used are: (The values used are used as an example to ensure the parameter and its

definition makes sense.) [1]

19

Population Size = 100: Number of GA solutions generated in each step.

Elite Population Size = 10: number of elite population of trail solutions in the

main GA population.

Number of Crossover Points = 4: The number of cut points in each parent

chromosome while crossing over with the other parent.

Probability of Crossover = 95 %: The probability of crossover operation being

performed at the cut point in the genetic algorithm.

Probability of Mutation = 1.5 %: The probability of random change in Genetic

Algorithm solution.

Probability of Creeping Down = 65 %: The probability that a decision value in

child chromosome will mutate and result to a smaller value.

Probability of elite mate = 0.5: The selection probability of an elite

chromosome for the usage in next generation in the genetic algorithm.

Probability of Winner = 95%: The probability of selecting the most fit

chromosome within a two chromosome tournament in the process of parent

selection.

20

3.2.3.6 STOPPING CRITERIADuring optimization the code operations are repeated up to when the expected results are

obtained. For the process to identify when to terminate the selecting process, a stopping criterion

is set to ensure the expected objective is achieved before the whole process is terminated. The

terminating conditions are:

Maximum Generations = 1000: The maximum generation number that is allowed to

conduct the genetic algorithm process.

Maximum Trials = 100000: The maximum number of optimized run trials that can be

performed.

Maximum Non Improvement Generations = 200: The maximum number of

generations allowed indicating non-improvement in the fitness results obtained.

The GA process can be represented using a flow chart, figure 5.3.6, to show the various steps

involved in the optimization process using GA. This generally simplifies the whole process.

21

Figure 3.6 Genetic algorithm process.

3.2.4 PARTICLE SWARM OPTIMIZATIONParticle swarm optimization (PSO) is a population based algorithm. PSO is a searching algorithm

that is derived from simulating the social behavior of birds. In PSO, individuals, known as

particles, “fly” through multi dimensional search space with the aim of obtaining the optimal

solution or the best fit particle [14]. Position of a particle within the search space and how it

changes is obtained from the social-psychological tendency of individuals to copy the success of

other individuals. Particle behavior is in some way a reflection of the behavior of the particles

around it. The particle behavioral changes are thus influenced by the interaction a particle has

with its neighbours and its experience within a given space.[8]

22

PSO is a simplified algorithm which can easily be implemented. It is effective in optimizing a

wide range of optimization functions. The PSO concept is derived from genetic algorithm and

evolutionary programming. The modification towards obtaining the optimal value is close to the

cross over process in GA. However PSO has a unique concept that it applies in optimization.

This concept involves flying potential solutions through hyperspace and then they are accelerated

towards “better” solutions. Success of PSO relies in the agents’ tendency to rush through their

target. Factors of stochastic allow thorough search of spaces between regions that have been

found to be good, and the momentum.

PSO is a widely used approach to obtain solutions to industrial optimization problems. When

compared to GA, PSO is found to be flexible, easy to use, adaptable in discrete and even

continuous optimization variables. It has a high execution speed and is very straight forward in

implementation thus is the most ideal in optimization compared to other tools.

3.2.4.1 PSO PROCESSPSO research and analysis is carried out in the following approach: [8]

1. The mixed integer PSO algorithms are evaluated.

2. The evaluation results are not satisfactory, therefore a binary PSO optimization algorithm is

developed for this research. The developed algorithms are tested to ensure they are better than

the original algorithms.

3. An optimal pump capacity selection model is defined. This is used to select optimal pump

capacities to ensure that the operational energy cost is minimized with respect to the tariff used,

demand and system constrains. The pump capacities and optimal LS schedule to ensure the

maximum of the combined EE and LS is achieved.

4. Simulations are conducted under different tariff structures and system limitations. The results

obtained are then analyzed.

5. Through the simulation obtained we identify how rigid the optimal design is. This helps us

develop a flexible pump operation control system which, as was mentioned previously, is the

variable speed drive on/off controller.

6. The open-loop optimal control model is obtained for the variable speed drive on/off controller.

23

7. the approach for coming up with a pump flow-power function that can predict required input

power for different flow rate or motor rotation speed of a pump are derived. The measurement

approach and the theoretical approach are used.

8. The tests carried out are used to evaluate the performance of the VSD on/off controller.

Different tariffs are used to carry out simulation for a given case study. Tests are conducted to

evaluate the performance of the VSD on/off controller. Different tariff structures are applied.

9. The four common pump controls strategies include valve control, level based on/off control,

VSD control and optimal on/off control. Simulated energy costs of the four controls under

different tariff structures obtained are then compared with respective VSD on/off controller

energy costs.

These guidelines help us to optimally use the particle swarm method and achieve the required

results. However modification can be done to suit different scenarios.

3.2.4.2 BENEFITS OF PSO- It uses the POET framework to define a pumping system efficiency improvements

strategy

- An optimal pump selection model is formulated based on both energy efficiency and load

shifting

- Combination of EE & LS achieves greater cost reduction

- The power prediction function derivations formulated provide accurate estimations and

thus can easily be used in optimization algorithm

3.2.4.3 CHALLENGES OF PSO- Maintenance cost of the pump operation is not considered in this research.

- Pump input power derivations are obtained from estimates and thus cannot be 100%

accurate.

- Current pump input power analysis functions apply only to fresh water pumping

systems. This therefore means modification have to be done for other pump applications,

such as in oil pumping.

24

- Pump aging effects are not considered. This is also a major contributor in determining the

efficiency of pumps.

- Coming up with the optimization models and binary PSO algorithm is a challenge.

25

CHAPTER 4

PROBLEM FORMULATION

4.1 FUNDAMENTAL OF PSOPSO is based on the analogy of birds’ movement. It searches for the global maximum or

minimum of a cost function by simulating movement and interaction of particles in a swarm [8].

A particle position determines a possible solution of the optimization problem. Each particle

represents a complete solution set. A new set of particle position is computed for each particle

using the given equation:

, ( + 1) = , ( ) + , ( + 1) (4.1)

Where;

, ( )- Value of the b-th dimension of the a-th particle at the k-th iteration

, ( )- Velocity of b-th dimension of the a-th particle at the k-th iteration

, ( + 1) − . , ( ) + . . , − , ( ) + . . − , ( ) (4.2)

Where;

- Inertia coefficient, - Social rates coefficients, which control the pull to the global best position

- function that generates uniformity distributed random pumbers in the interval from 0.0 to 1.0

, -current best solution for the a-the particle

-current global best solution

The particle position for the ( + 1) − ℎ iteration is given as:

26

, ( + 1) = , ( ) + . , ( ) + . . , − , ( ) + . . −, ( ) (4.3)

Particle position and velocities are randomly assigned. The process of obtaining the fitness of the

particles and derivation of new particle positions are repeated until the stop criteria is attained. A

description of the mixed integer PSO algorithm formulation used to solve the optimization

problems is as follows [14]:

Step 1

Initialization – continuous dimensions of a particle are initialized with a random value within a

set of upper and lower limits. The initialization of binary dimensions is as shown below.

, = + − = 1… . . = 1… (4.4)

Where; −Lower and upper limit of the continuous variable

- total number of continues variable dimensions in the particles

, 1 > 0.5 = 1 … .0 ≤ 0.5 = + 1… . (4.5)

Where;

- Total number of dimensions in the particles. This is equal to the sum of the number of binary

and continuous dimensions.

Particle velocity , for the continuous dimensions are initialized, with a range of between

and . Previous state of the binary dimensions, , (−1) , has to be initialized with a random

binary value and are initialized. Variables , , are initialized with a large value.

Step 2

27

The conditions for stopping criteria are checked to see if they are met. If so, the process goes to

step 7, else to step 3

Step 3

Fitness of each particle is computed. is the summation of two components; the objective

function fitness , and the constraint fitness . Objective function fitness is obtained by

substituting the a-th particle into the objective function. The constraints fitness is calculated

depending on the degree of constrain violation.

This is obtained by: = ∑ ∑ ( + , , ) (4.6)

Where;

and , are constants.

, , - amount of violation caused by the c-th constraint caused by the particular dimensions

Step 4

are determined. The purpose is to find the particle that results in the minimum

fitness value.

fitness of each particle, is compared to the best fitness value of that particle, . If is

smallest then , will be replaced by . replaces , which is the storing

point of the particle position .

is compared to the global best value . if is identified to be smaller than ,will be replaced by and which stores particle position of is replaced by .

Step 5

28

Determine the new particle position for the next iteration.

Step 6

Increment the iteration number by 1 and go back to step 2.

Step 7

The output is as the lower calculated operating, cost and as optimal control strategy.

4.2 MODEL SELECTION AND TESTINGThis optimization algorithm calculates optimal pumping capacities at different levels of a multi-

level pumping system based on an optimal operational strategy under different tariff structures,

water demand and reservoir sizes. An example of a multilevel pump set up is shown in figure

3.3. In this analysis optimal pump selection focuses on fixed speed pumps since an optimally

selected pump should not require more investment on flow rate adjustment such as values and

variables.

4.3 OPTIMIZATION ALGORITHM

The purpose of the pump selection algorithm is to obtain an optimal a pump capacity that is

optimal for use in different aspects, which will result to minimum cost that is incurred by the

energy in use. Large capacity pumps are easier to shift operation from the peak period. This

therefore adds to the aim of cutting on cost. However, pumps with large capacity have poor

energy efficiency and always have high energy consumption. The selection model analyses the

effect of pump capacity on energy efficiency and load shifting. The objective function of the

optimal pump capacity selection model is:

, , = ∑ ∑ ( ) , + (4.7)

Where

- level indicator and = 1,…- total number of levels

29

-number of control intervals in which all the operation parameters can be assumed

- number of repeating cycles of duration within the control horizon and the product of and

represents the total number of control intervals in control horizon.

- the i-th discrete control interval and i=1…1c, - on/off status of pump at the r-th level and i-th control interval

- capacity of the pump at the r-th level in /ℎ( )- capacity power function that finds the pump input power corresponding to the pump

capacity.

- the time of use energy cost for the i-th control interval

- maximum demand charge factor in Ksh/KW

- the function that finds maximum demand

Optimal values of , and should be solved by the optimization algorithm over the control

scope. is the sum capacity value of the r-th level. This is left for the supply system designer to

decide whether this capacity is achievable, and the number of pumps required as a combination

to achieve it. The period of the control scope is represented by the product value of and and

should be equal to a month. For instance, consider a month with 30 days and an operation

repeated in time of 24 hours, and will be 24 and 30 respectively.

Maximum demand (MD) is a measure of the averaged demand in KVA during any complete half

hour integrating period. The power over a given period of half an hour interval is computed as:

2∫ ( ).(4.8)

Where;

-time( )- Instantaneous power consumption, in KW as a function of time.

30

T- Starting point – half a period.

Figure 4.1 power consumption

Figure 4.1 shows the power consumed within a given period with a time span of 1 hour. The

assumption made is that the operation of the pump and pump power consumption, ( ), is taken

as a constant unit within a given interval.

Consider conditions of control interval duration greater than or equal to maximum demand

integrating period and where ( ), remains constant within a control interval, we have:( ) = { ( )}Where;

- this is the maximum value function

Control interval is taken to be one hour throughout. The time based tariff varies on an hourly

basis. When a longer duration is used, there is a reduction in the wear and tear from regular

operational adjustments.

Thus the maximum demand value is given as= ∑ ( ) , : = 1… . . (4.9)

31

Input power of a fixed speed pump can be computed using the hydraulic equation shown

= . . (4.10)

Where;

-pump input power in KW.

- Pump capacityℎ- generated pressure head by pump in m.

- pump efficiency

9.81 and 3.6 are constants.

The relationship between the pump pressure head and capacity can be shown using the system

curve shown on figure 4.2.

Figure 4.2 head capacity relation

32

System curve is a representation of the expected pump pressure from the pump to achieve a

certain flow rate. This is the pressure that should push water to the destination while at the same

time overcoming the pipe flow resistance between pump and destination. This is a fixed

relationship irrespective of the type of pump.

For of multi-level pumping system, the pipe arrangement at each level is different. This therefore

means for every level of pumps there is a different system curve A system curve can be obtained

using a second order quadratic equation; ℎ = + + (4.11)

where;

A, B, C are unique values for every system curve.

The system efficiency is taken to be constant the power factor is taken as unit.

The second order equation is substituted into the input power equation to obtain capacity power

function.

Water levels in the reservoirs should be within the set limits i.e. the upper and lower reservoir

limits, all through the operation. The optimization algorithm is set within the following

constraints: ≤ ≤Where;

- Reservoir indicator and = 1,… , ; where is total number of reservoir.

- level of the − ℎ reservoir at the − ℎ control internal.

and - lower and upper level limit of the − ℎ reservoir.

To obtain the wetter level in the reservoir at the beginning of the ( + 1) − ℎ operational

interval we have:

33

, + 1 = , + , , − ,Where, – flow rate of the − ℎ pumb at the − ℎ reservoir at the − ℎ control interval, - amount of water that flows in/out of the − ℎ reservoir from sources other than thepumps in /ℎ .

4.4 SIMULATION RESULTS AND DISCUSSIONWe consider one pump and one reservoir so that the capacity selection ability of the algorithm

can be the main focus. Three simulations are performed:

Simulation during high demand tariff with insufficient reservoir storage volume.

Simulation during low demand tariff with enough reservoir storage volume.

Simulation during high demand tariff with insufficient reservoir storage volume.

During this analysis we ignore the maximum demand charge so as to demonstrate a balanced

energy efficiency and load shifting capacity selection.

34

Figure 4.3 Pump activation time

Figure 4.4 reservoir levels

35

4.4.1 HIGH DEMAND TIMEAn optimal simulation was conducted under high demand season tariff. The lower reservoir limit

was set to 300m3. The upper limit was set at 1200 m3. Ic is 24 hours, the demand is set to be

constant at 70m3/hour i.e.

di =70 v

The optimal capacity of the pump was obtained as 102.12m3/hr and the operation schedule and

change in reservoir volume are shown in figure 4.3 and figure 4.4 respectively.

From Figure 4.3 it is seen that the pump has enough capacity to allow an entire load shift out of

the peak period. In figure 4.4 the reservoir volume is at minimum level during the 23rd hour,

which is the end of the peak period. This shows the pump capacity is capable of shifting the load

entirely from the peak period.

To show that the results obtained are optimal, simulations are conducted to study energy cost

changes related to pump capacity selection. The simulation is carried out to compute the

operational energy costs for different pump capacities ranging from 70m3/hr to almost twice the

value. The parameters remain unchanged from the previous optimal selection simulation. Figure

4.5 shows a plot of simulated energy costs of the optimal operations of the different pump

capacities.

36

Figure 4.5 energy cost over capacity

An ideal choice of pump capacity for an EE only optimal design algorithm ranges above 70m3/hr

as shown on figure 4.5. The corresponding energy costs are very high. Increase in pump capacity

increases the size of loads that can be shifted out of the peak hour and the energy cost is reduced.

The Optimal pump capacity appears to be averaging 102m3/hr as can be seen on figure 4.5.

When the pump capacity hits 102m3/hr, the entire load is shifted out of the peak hours and these

results to cost reduction. Any further shift beyond the optimal level causes a relative increase in

the cost of energy. This brings out the fact that energy efficiency and load shifting are opposites

of each other. When working on improving energy efficiency there is a resultant negative effect

on the load. Therefore, optimal capacity selection is meant to balance energy efficiency and load

shifting to bring out the better of the two.

4.4.2 LOW DEMAND TIMEIn the next simulation the low demand tariff is considered. The other simulation parameters

remain unchanged so as to ensure proper comparison is done between the high demand and low

demand. The optimal capacity is obtained as 70.01m3/hr. This is similar to the demand.

37

Therefore, there will be no load shifting despite the high cost in electricity. The results are

further analyzed to prove that the value obtained is correct.

In the analytical simulation carried out the tariff used is the low demand tariff. Observations are

made on how the energy cost changes with a change in the pump capacity. The pump capacity

with minimized operational energy cost is seen to be 70m3/hr. this shows that an increase in

pump capacity with the aim of carrying out load shifting is not always ideal, especially when

tariff is considered. The capacity increase that will sustain a load shift out of peak hours may

result to a major increase in input power of the pumps. This will bring about a higher cost than

the saving done in shifting loads.

Figure 4.6 low tariff pump activation

4.4.3 RESERVOIR LIMITSCases arise when the reservoir capacity is incapable of supporting massive load shift. We

simulate with a reservoir limit capped at 800m3 while the lower limit remains 300m3. The

optimal capacity value obtained is 91.68m3/hr. This is a lower level. Load shifting is dictated by

reservoir size, therefore a high capacity pump will not be required. Thus, the algorithm picks the

smallest pump capacity capable of achieving the limited load shifting.

38

Figure 4.7 low tariff reservoir size

The optimal operation and the respective reservoir level changes are plotted in figure 4.6 and

figure 4.7 respectively. Load shifting is limited in a significant way by the reservoir size. The

pump capacity of the installed pump allows the full utilization of the storage capacity.

39

CHAPTER 5

CONCLUSIONOptimal pump scheduling is vital in many ways more than those that have been discussed in this

report. Various systems in modern day today require optimization in their operation to achieve

the best possible results. However, coming up with the best optimization tool can be a challenge

especially if it is required that al constraints are included in the optimization tool. This can act as

an impediment and thus end up discouraging people against going forward and optimizing their

systems. To identify the best tool, deep research has to be carried out keeping in mind the main

factor that is intended for optimization.

The tool used in this project, PSO, is flexible considered to other tools of optimization such as

genetic algorithm, because it allows you room to carry out optimization in bits. It is a kind of a

micro approach in the sense that it allows you to optimize small sections of a whole system

which in the long last lead to effectively optimized approach. For instance the results obtained

are just a section of a whole that can be obtained. However, this should not make it sound as

though it is a less efficient tool.

Various problems were encountered during this project research. Identifying a local case study

for use in this report was a tall order. Various entities were uncooperative, not out of malice but

because of their fear of releasing information they consider vital and which can sabotage their

operations if it falls into the wrong hands. Several attempts were made to consult various entities

that deal in fields that relate to this project, but all was in vain. This did not stop the research

anyway because a simulated case was used. The simulated case used did not affect the objective.

As seen above, the ultimate goal was to show that a given system, irrespective of which it is,

with the set down conditions, can be optimized and made to improve in a manner that is

intended.

The project focused solely on water supply systems. However, this does not mean that

optimization can only be done in water supply. There are other related fields that can be ventured

into and optimization carried out. Fields like the oil supply system, gas supply system and many

more. All this can work better under optimized systems.

40

5.1 RECOMMENDATIONUltimately, the objective of the project was achieved. The energy of the simulated system was

kept in check while ensuring that the load demand was at the least cost possible. However, this

does not mean this the best that there can be. More research can be done to carry out

optimization as a whole without looking at it in sections. This will improve the factors further

and achieve a more efficient system. Other optimization techniques can be used to achieve an

optimally scheduled system and then compared to identify the best tool of use. Nonetheless,

irrespective of the tool used, optimization sorely depends on how the parameters are set.

Parameters determine the kind of results to be obtained.

41

REFERENCE1. Bentley WaterCAD User’s Guide, Bentley Press, 2009

2. Doruk, B. L.,” Identifying Efficient Pump Combinations on Water Distribution Networks

Management”, 2001.

3. Curley, R. “New Thinking About Pollution”, Britannica Educational Publishing, USA,

2011.

4. Karassik, I. J., Messina J. P., Cooper, P. and Heald C. C., “Pump Handbook”, McGraw-Hill,

New York, 2008

5. Mäckle, G., D.A. Savic and G.A. Walters “Application of Genetic Algorithms to Pump

Scheduling for Water Supply”, Genetic Algorithms in Engineering Systems: Innovations and

Applications, IEE Conference, GALESIA, 1995.

6. Kenya Power Company

7. Energy Regulatory Board of Kenya

8. S. Kitayama, K. Yasuda, “A Method for Mixed Integer Programming Problems by

Particle Swarm Optimization,” Electrical Engineering in Japan, 2006.

9. M. Moreno, P. Carrion, “Measurement and improvement of the energy efficiency

at pumping stations,” Biosystem Engineering, vol.98,, 2007.

10. X. Xia, J. Zhang, “Energy efficiency and control systems - from a POET perspective,” in

IFAC Conference on Control Methodologies and Technology for Energy Efficiency, Vilamoura,

Portugal, March 2010

11 D. Loughran, J. Kulick, “Demand-side management and energy efficiency in the United

States,” The Energy Journal, vol. 25, no. 1, 2004.

12 Sulzer Brothers LTD, Sulzer Centrifugal Pump Handbook, New York: Elsevier Science

Publisher LTD., 1989.

42

13. E. Kamdem, “Measurement and verification on combined load management and energy

efficiency project,” http://www.eskom.co.za/content/CombinedLM-EE.pdf.

14. K. Yang, J. Zhai, “Particle Swarm Optimization algorithms for optimal scheduling of water

supply systems,” in 2nd International Symposium on Computational Intelligence and Design,

Shangsha

15. J. Tolvanen, “Life cycle energy cost savings through careful system design and pump

selection,” World Pumps, July 2007

16. M. Lopez-Ibanez, “Multi-objective optimization of the pump scheduling problem using

SPEA2,” Evolution computation, vol. 1, 2005

43

APPENDIX%MATLAB code for optimal pump capacity selection model%Algorithm initialization parametersiteration=30000; particles = 50; dimension = 24; c1 = 2; c2 = 2;g_best=10000000; best_val=10000000;%tariff=[0.1187;0.1187;0.1187;0.1187;0.1187;0.1187;0.1411;0.8205;0.8205;0.8205;0.1411;0.1411];%High demand tarifftariff=[0.118700000000000;0.118700000000000;0.118700000000000;0.118700000000000;0.118700000000000;0.118700000000000;0.141100000000000;0.820500000000000;0.820500000000000;0.820500000000000;0.141100000000000;0.141100000000000;0.141100000000000;0.141100000000000;0.141100000000000;0.141100000000000;0.141100000000000;0.141100000000000;0.820500000000000;0.820500000000000;0.820500000000000;0.820500000000000;0.118700000000000;0.118700000000000;];%Low demand tarifftariff= [0.104900000000000;0.104900000000000;0.104900000000000;0.104900000000000;0.104900000000000;0.104900000000000;0.138300000000000;0.262800000000000;0.262800000000000;0.262800000000000;0.138300000000000;0.138300000000000;0.138300000000000;0.138300000000000;0.138300000000000;0.138300000000000;0.138300000000000;0.138300000000000;0.262800000000000;0.262800000000000;0.262800000000000;0.262800000000000;0.104900000000000;0.104900000000000;];%minmum and maximum pump selection rangeAVD=70; MAXD=120;%Minimum and maximum reservoir levelAVR=500; MAXR=1000; LL=500; UL=1000;%Initial reservoir volumeLVo=500;%demand (m^3)/hour%D=[60;60;60;60;100;100;100;100;60;60;60;60];D=[70;70;70;70;70;70;70;70;70;70;70;70;70;70;70;70;70;70;70;70;70;70;70;70;];%maximum demand costdc=66.5;%system equation used to compute the input power of the pumpsystem=[0.00112946428571429,0.00228214285714281,3.99785714285715];%efficiencyeff=0.8;g_best=10000000; best_val=10000000;% Inialization of the variables and velocityfor i=1:particlesfor j = 1:dimension%initialization of the binary variables the on/off scheduleif rand>=0.5particle_position(i,j) = 1;elseparticle_position(i,j) = 0;endif rand>=0.5prev_position(i,j) = 1;elseprev_position(i,j) = 0;

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endp_best(i,j) = particle_position(i,j);cost(i,j)=0;pbest(i,(j)) = particle_position(i,(j));exceed(i,j)=0;end%initialization of the continous variables the pump capacityparticle_position(i,dimension+1) = AVD+rand*(MAXD-AVD);particle_velocity(i,dimension+1) = AVD-rand*(2*AVD);prev_position(i,dimension+1) = AVD+rand*(MAXD-AVD)/1.5;endfor i=1:particlesp_best_fitness(i)=10000000;fitness(i)=0;endfor k=1:iterationfor i=1:particles

fitness(i)=0;end%compute solution and fitness with constraintsfor i = 1:particlesvol(i,1)=LVo;for j=1:dimensionexceed(i,j)=0;end%Compute the power consumption for a particular pump capacity%using the hydraulic equationhead(i)=system(1)*(particle_position(i,(dimension+1)))^2;+ system(2)*(particle_position(i,(dimension+1)))+system(3);power(i)=head(i)*(particle_position(i,(dimension+1)))/3600*9.81/eff;for j = 1:dimension%compute the cost of one set of 24 hour flow manangement%for one particlecost(i,j)=power(i)*tariff(j)*particle_position(i,j);fitness(i)=fitness(i)+cost(i,j);%compute the reservoir volume and determing whether constaint%is violated or not%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%vol(i,(j+1))=vol(i,j)+particle_position(i,(dimension+1))*...particle_position(i,(j))-D(j);if vol(i,(j+1))<LLexceed(i,j)=0;exceed(i,j)=LL-vol(i,(j+1));fitness(i)=fitness(i)+1+0.05*exceed(i,j);endif vol(i,(j+1))>ULexceed(i,j)=0;exceed(i,j)=vol(i,(j+1))-UL;fitness(i)=fitness(i)+0.8+0.05*exceed(i,j);end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%endMD=power(i)*dc;fitness(i)=fitness(i)*30+MD;

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fitness(i)=fitness(i)/30*365*15;end%determine p bestfor i = 1:particlesif fitness (i) <= p_best_fitness(i)p_best_fitness(i) = fitness(i);for j = 1:(dimension+1)p_best(i,j)= particle_position(i,j);endendend%determine gbest[g_best_val,g_best_index] = min(fitness);for j = 1:(dimension+1)g_best(j) = particle_position(g_best_index,j);endif g_best_val<best_valbest_val = g_best_val;for j = 1:(dimension+1)best_position (j) = particle_position(g_best_index,j);endfor j = 1:(dimension)best_exceed(j) = exceed(g_best_index,j);endend% Determine the new paritcle position and velocityfor i = 1:particlesfor j = 1:dimensioncurrent_position(j) = particle_position(i,j);storage_position(j) = particle_position(i,j);position_indication = current_position(j)+prev_position(i,j);+g_best(j)+p_best(i,j)-2.444+rand*(2*2.444); %#ok<*VUNUS>if position_indication>=2particle_position (i,j)=1;elseparticle_position (i,j)=0;endendfor j = 1:dimensionprev_position(i,j) = storage_position(j);endcurrent_position((dimension+1)) =...particle_position(i,(dimension+1));particle_velocity(i,(dimension+1)) =...((particle_velocity(i,(dimension+1))*(1-k/iteration)) +...c1*rand*(p_best(i,(dimension+1))-...current_position((dimension+1))) +...c2*rand*(g_best((dimension+1))-...current_position((dimension+1))))/1.8;%particle_velocity(i,(dimension+1)) =((particle_velocity(i,(dimension+1)))...+ c1*rand*(p_best(i,(dimension+1))-...current_position((dimension+1)))...+ c2*rand*(g_best((dimension+1))-...

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current_position((dimension+1))))/(1.1);if particle_velocity(i,(dimension+1))>(AVD/5)particle_velocity(i,(dimension+1))=(AVD/5);endif particle_velocity(i,(dimension+1))<-(AVD/5)particle_velocity(i,(dimension+1))=-(AVD/5);endparticle_position (i,(dimension+1)) =...current_position((dimension+1));+ particle_velocity(i,(dimension+1));endend