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Link¨oping university Department of Management and Engineering Applied Thermodynamic and Fluid Mechanics Master Thesis 2021|LIU-IEI-TEK-A–21/04051-SE

ORC systems for small scale

energy production

Improving the prediction of electricity production

of ORC turbines under varying loads.

Kristina Pettersson

Academic supervisor: Hossein Nadali Najafabadi Industrial supervisor: Joakim Wren

Examiner: Ingrid Andersson

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Abstract

In order to have a sustainable, resource-efficient energy system and no net emissions of greenhouse gases by 2050, energy efficiency is one important aspect to reach this goal and develop a long-term sustainable energy system. As part of a solution to increase energy efficiency in society, Organic Rankine Cycle (ORC) systems can have a far reaching effect by utilizing low-grade heat to produce electricity.

The market of ORC systems is currently growing and in Sweden and other Nordic countries, the growth can be attributed to extensive use of district heating. Since the available heat at district heating network changes with season, and is limited by the required supply temperature to the district heating network, this project focused on improving the prediction of electricity production of ORC systems under these varying loads. The investigation started with analysis of off-design performance by obtaining compensation factors which can be used to approximate losses due to part load operation. The calculated compensation factors were then used in the contin-ued investigation to seek the optimal interval of output temperature from the ORC condenser. By using the compensation factors to estimate the electricity production during part load, the right balance between part load and using most of available heat was found, determining the design point to maximise the annual electricity production.

The project also investigated how large pressure ratios were possible for different generator sizes, modules and stages of the turbine. Based on the calculations, the overall conclusion was that module T434 was good to use for almost all conditions by only changing the number of stages. As a general trend however, larger modules and an increased number of stages resulted in a higher possible pressure ratio over the turbine.

Finally, the project investigated how performed calculations agreed with measured data from an installed ORC system at a district heating plant. Analysis of the measured data and theoretical values from Againity’s turbine program were found to be in good agreement with each other.

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Sammanfattning

F¨or att uppn˚a en h˚allbar, resurseffektivt energisystem och inga nettoutsl¨app av v¨axthusgaser fram till 2050, ¨ar energieffektivisering en viktig aspekt f¨or att uppn˚a detta m˚al och utveckla ett l˚angsiktigt h˚allbart energisystem. Som en del av en l¨osning f¨or att ¨oka energieffektiviseringen i samh¨allet kan ORC-system (Organic Rankine Cycle) ha en l˚angtg˚aende effekt genom att anv¨anda l˚agkvalitativ v¨arme f¨or att producera el.

Marknaden f¨or ORC-system v¨axer och i Sverige och andra nordiska l¨ander kan tillv¨axten h¨anf¨oras till omfattande anv¨andning av fj¨arrv¨arme. Eftersom den tillg¨ ang-lig v¨armen fr˚an fj¨arrv¨armen¨atet ¨andras med s¨asong och begr¨ansas av framledning-stemperaturen till fj¨arrv¨armen¨atet, fokuserar detta projekt p˚a att f¨orb¨attra uppskatt-ningen av elproduktion fr˚an ORC-turbiner under olika v¨armelaster. Unders¨ okning-en startade med att analysera ORC-turbinokning-en prestanda utanf¨or sitt designomr˚ade, genom att ber¨akna kompensationsfaktorer som kan anv¨andas f¨or att approximera f¨orlusterna vid dellast. De ber¨aknade kompensationsfaktorerna anv¨andes sedan i den fortsatta unders¨okningen f¨or att ber¨akna det optimala intervallet f¨or ut-temperaturer fr˚an ORC - systemets kondensor. Genom att anv¨anda kompensa-tionsfaktorerna f¨or att uppskatta elproduktionen under dellast, hittades r¨att balans mellan dellast och anv¨andning av tillg¨anglig v¨arme, vilket best¨amde designpunkten f¨or att maximera den ˚arliga elproduktionen.

F¨or att s¨akerst¨alla en bra turbinkonstruktion unders¨okte projektet ocks˚a hur stort tryckf¨orh˚allande som var m¨ojligt f¨or olika generatorstorlekar, moduler och steg i tur-binen. Baserat p˚a ber¨akningarna var den ¨overgripande slutsatsen att modul T434 var bra att anv¨anda i n¨astan alla f¨orh˚allanden genom att bara ¨andra antalet steg. Som en allm¨an trend resulterade dock st¨orre moduler och ett ¨okat antal steg i ett h¨ogre tryckf¨orh˚allande ¨over turbinen.

Slutligen unders¨okte projektet hur utf¨orda ber¨akningar ¨overensst¨amde med m¨atdata fr˚an en installerad ORC-turbin vid ett fj¨arrv¨armeverk. Analys av m¨atdata och teoretiska v¨arden fr˚an Againitys turbinprogram och Cycle Tempo var i god ¨ overens-st¨ammelse med varandra.

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Acknowledgements

I would like to express my very great appreciation to both my supervisors Hossein Nadali Najafabadi and Joakim Wren for your teaching, comments and valuable guidance throughout the entire project. I am truly gratefully for your help and availability whenever I needed to discuss anything. I would also like to thank the company Againity for giving me the opportunity to work on this project and im-proving my knowledge of ORC turbines.

Last but not least, I would give my deepest gratitude to my loving and caring fiance Florian Bock. Without your encouragement and support, the completion of my project would not have been possible.

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Nomenclature

Abbreviations and Acronyms

Abbreviation Meaning

AGT Againity’s turbine program

APES Againity Performance Evaluation Software

DHN District Heating Network

ORC Organic Rankine Cycle

RPM Revolutions per Minute

RMS Root Mean Square

Latin Symbols

Symbol Description Units

a Annual savings [SEK/year]

C Arbitrary constant [−]

cp Constant pressure specific heat [kJ/kg K]

h Specific enthalpy [kJ/kg]

G Hardware price [SEK]

m Mass [kg]

P Pressure [kP a or bar]

q Heat transfer per unit mass [kJ/kg]

Q Total heat transfer [kJ ]

˙

Q Heat transfer rate [kW ]

T Temperature [◦C or K]

w Work per unit mass [kJ/kg]

˙

W Power [kW ]

Greek Symbols

Symbol Description Units

η Efficiency [−]

Subscripts and superscripts

Abbreviation Meaning p pump th thermal t turbine i inlet o outlet

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Abbreviation Meaning

D Design point

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Contents

1 Introduction 1

1.1 Background . . . 1

1.2 Aim and Scope . . . 3

1.3 Delimitations . . . 4

1.4 Sources . . . 4

2 Theory 5 2.1 Organic Rankine Cycle . . . 5

2.1.1 Connection of ORC system . . . 7

2.1.2 Cycle efficiency . . . 8

2.2 District heating network . . . 8

2.2.1 District heating networks in Sweden . . . 8

2.3 Stodola’s Law of the Ellipse . . . 9

2.4 Turbine design . . . 11

2.4.1 Turbine losses . . . 11

2.5 Linear model for regression . . . 12

2.5.1 Least squares method . . . 12

3 Method 13 3.1 Compensations factors . . . 14

3.2 Output temperature . . . 16

3.3 Turbine design . . . 19

3.4 ORC system performance . . . 20

4 Results 22 4.1 Compensation factors . . . 22

4.2 Output temperature . . . 23

4.3 Turbine design . . . 26

4.4 ORC system performance . . . 32

5 Discussion 36

6 Conclusions 39

7 Outlook 40

8 Perspectives 41

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1

Introduction

In the chapter Introduction, the background and problem analysis are presented, con-taining the purpose of the work and the goals that the project is expected to achieve. Furthermore, the delimitations and the assessments of used sources are also described and discussed.

One of Sweden’s environmental objectives is to have a sustainable, resource-efficient energy system with no net emissions of greenhouse gases by 2050 [1]. Energy effi-ciency is one important aspect to reach this goal and develop a long-term sustainable energy system. According to a study by the International Energy Agency (IEA) and Nordic Energy Research (NER), energy efficiency requires first order priority if the transition to a climate-neutral energy system is to succeed [2].

The transition to a more sustainable energy system demands more renewable energy sources, such as solar- and wind power. With a growing share of intermittent energy sources, other problems such as power outage will likely occur. Investigation of the energy balance in the Swedish electricity market have shown that cold weather con-ditions in combination with a high electricity demand might call for harsh measure such as disconnecting users from the grid to avoid large scale power outages [3]. The growing electricity demand in combination with the increasingly stricter sustainabil-ity requirements entails an increased need for locally produced base power in the system.

As part of a solution, Organic Rankine Cycle (ORC) systems can have far reaching effect both in the transition to a more climate neutral energy system and to increase energy efficiency in society. Since ORC-technology can utilize low-grade heat to produce electricity, the system can be used in a variety of areas such as in district heating plants, industries with waste heat and for small-scale waste incineration plants [4].

1.1

Background

The development of ORC technology started in the 19th century, when Carnot predicted the possibility of using other mediums than water for transfer of energy, yet the technology could not be implemented until tools for thermodynamic analysis were developed much later during the 20th century. Effective use of ORC-technology with low-grade heat sources initially started as research projects at universities and small companies, and in recent decades only a hand-full of companies have succeeded to turn this area of research into a commercial business. [5]

The market of ORC systems is currently growing and since the technology can be used in a wide range of applications, including different operation constraints and temperatures, the design of the ORC-system requires customized solutions [6]. In Sweden and other Nordic countries, this growth can be attributed to the extensive

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use of district heating. For optimal performance of an ORC system, careful analysis of cycle configurations, power efficiency, off-design performance, dynamic behaviour and economic aspects are crucial.

Performance optimization has been intensely studied, and many investigations have focused on selecting a proper working fluid to achieve the highest possible efficiency [7][8][9]. Dai et.al. [10] also focused on examining working fluids, but in contrast to others they focused on analysing working fluids for ORCs at optimal conditions. The investigation showed that the fluid’s saturation curve had a large impact on the power output. Working fluids with a negative slope of the vapor saturation curve, so called dry mediums, had a greater turbine power output with an increasing turbine inlet temperature. On the other hand, working fluids with a non-negative slope re-quire the turbine inlet temperature to be as low as possible above the fluids boiling point, to achieve greater power output.

Analysis of off-design performance is important when the ORC is installed at a heat source with varying operating conditions. Information about off-design behaviour of the system enables designing a more suitable configuration of the system [6]. For instance, if the ORC is going to be installed at a heating plant where the available heat changes with the season, the size of the system should be adopted in order to optimize the annual electricity production during the year. To predict how much electricity the ORC system will generate during part load, a traditional way is to use Stodola’s ellipse law. This describes the connection between mass flow, pressure and specific volume and can be used to investigate how the turbine will perform with changing operating conditions [11]. A simpler and more effective approach is to use compensation factors for approximation of the losses due to part load. In cases when the heat load varies throughout the year, such as at district heating plants, compensation factors can heavily decrease the number of calculations that are needed to predict the annual electricity production. Instead of making a separate calculation for each month, one calculation can be performed for the design point and the compensation factors can be used for all the part load scenarios. Correct compensations factors correlating to the off-design performance are therefore crucial to effectively predict the annual electricity production.

Furthermore, ORC systems installed at heating plants tend to be limited by the necessary supply temperature of the district heating network. In order to still main-tain a high electrical efficiency and fulfil the temperature requirements, the output temperature from the ORC condenser needs to be optimized regarding this. The majority of conducted studies do not take such circumstances into account, since focus usually lays on heat produced from geothermal or solar sources [12] [13], where all of the heat is available for energy production.

The pressure and temperature conditions before and after the turbine are also im-portant to investigate, since this greatly affects the turbine performance and thereby how much electricity can be generated [14]. In cases when e.g. differences in both temperature and pressure are high, but the heat flow through the turbine is rel-atively low, the turbine efficiency tends to be rather low. Therefore, the pressure

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difference sometimes needs to be limited to a certain range to achieve a good turbine design with a viable efficiency. Optimizing and compiling results regarding these vi-tal parameters can speed up the workflow of future calculations, while also acting as a rule-of-thumb as to which cases have high enough profitability.

Finally, it is of great importance to compare performed calculations and simulations with actual measured data from already installed ORC systems to investigate if the calculations of the predicted electricity production need to be further improved.

1.2

Aim and Scope

In most cases, the customer hands over data of the available heat that can be used in the ORC system, temperatures of the hot water/steam and temperatures of the cooling water. Considering that this project will focus on heat sources with varying loads such as district heating plants, monthly heat data and supply and return tem-peratures from the district heating network are needed data for the calculations of estimated electricity production for each month. Since these calculations are used to investigate the potential electricity production at an early stage, they need to be computationally efficient, so that a range of different cases can be analysed quickly. Due to the wide variety of cases being tested at an early stage, the calculations do not need to be of the highest accuracy, and should instead give a coarse overview of which setups might be best suited.

The aim of this thesis is to improve the predictions when analysing how much elec-tricity an ORC system can generate. It is important to ensure that the calculations are consistent with the actual system performance and to get more accurate results when determining the profitability for the potential customers. Towards this aim, the work will answer four research questions, each investigating parameters that af-fect the prediction of the electricity production which is conducted as the first step in the sales process.

The project’s aim is summarised in the following research questions, which are anal-ysed in this report:

1. What are the compensations factors for prediction of electricity production at off-design operation?

2. What is the optimum interval of output temperatures of the ORC condenser in relation to evaporation pressure, condensation pressure, heat input and supply temperature to the district heating network to maximize the electricity production?

3. What condensation pressure in combination with evaporation pressure will achieve a reasonable turbine design (i.e., not too many stages, not to large diameters)?

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1.3

Delimitations

The calculations in this study will be performed in collaboration with the company Againity which use a dry working fluid in their ORC systems. This means that the performance will only be analysed with this type of medium. Furthermore, the temperatures and pressures that are going to be analysed will be limited to conditions suited for Againity’s ORC systems. This means that the turbine inlet temperature will be in a range between 90 to 145◦C, the condensation temperature between 5 to 90◦C and pressures between 2 to 20 bar.

1.4

Sources

To ensure that the theory is based on credible and reliable sources, this report is primarily based on peer-reviewed articles retrieved from Google Scholar. Since these types of sources are written by experts and also reviewed by other researchers within the same field before publication, this results in high quality and scientifically valid articles. The risk that the author of the article has a motive which could have influ-ence on the result is also minimized when using peer-reviewed articles. Secondly, the report contains interviews from experts on the ORC technology and turbine devel-opment from the company Againity, which also can be seen highly credible sources. Other sources used in this study have been relevant books that explains the fun-damentals of thermodynamics and linear regression. Input data to the calculations has been retrieved from Againity’s data base regarding heat load variations and temperatures at Nordic heating plants.

It is important to note is that some sources used in the report were retrieved from websites, despite the fact that the reliability is not as high as peer-reviewed articles. Since this data only was used to gain insight into the environmental goals and the Swedish energy market, this will not affect the quality of the study to a great extent. These sources come from the International Energy Agency, Svenska kraftn¨at and from the Swedish government which can be considered to be of high quality, as the texts on these websites are produced by government experts without personal or financial connections that could affect the content.

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2

Theory

This chapter presents the theory and concepts which the calculations in this report are based on. The theory section starts by explaining the basis of the ORC cycle and continues with describing how a district heating network is working. Furthermore, the chapter discusses the background to Stodola’s ellipse law, losses in turbines and finally describes the Least Squares method which can be used to analyze the relation-ship between two or more variables.

2.1

Organic Rankine Cycle

The Organic Rankine cycle (ORC) is based on the same principle of a conventional steam cycle, but instead of water, an organic working fluid is used to recover heat from the heat source. Since the working fluid has a lower boiling temperature than water, the ORC system can archive a high efficiency, even at smaller systems using low temperature heat sources such as waste heat, biomass combustion, solar- and geothermal heat [12] [13].

The configuration of the cycle consists at its simplest form of a pump, evaporator, turbine and condenser, see Figure 1. The working principle starts with pumping the working fluid into the evaporator, where heat is transferred to the fluid. The superheated vapor then enters the turbine where it expands and goes through the condenser, which rejects the heat to a cooling medium. [15].

Figure 1: Schematic of the ORC that consists of a pump, evaporator, turbine and con-denser. Note that both heating and superheating takes place in the evaporator.

Since the organic working fluids have other characteristics than water, the slope of the vapor saturation curve of the organic fluid can be positive (wet), negative (dry)

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or vertical (isentropic) in the T-s diagram. In this study a dry medium is used and the saturation curve can be seen in Figure 2.

Figure 2: T-s diagram for the simple ideal and real Organic Rankine Cycle [16]. The numbers correspond to the different points in the cycle shown in Figure 1. 1a, and 3a are the actual state. 2s and 4s are the corresponding states for the isentropic case.

In the ideal Organic Rankine cycle there are four processes that can be described: 1-2s Isentropic work in the pump.

2s-3 Isobaric evaporation and superheating, no pressure drop in the heat exchanger. 3-4s Isentropic expansion in the turbine.

4s-1 Isobaric condensation, no pressure drop in the heat exchanger.

With the assumptions above and steady-state conditions, the energy balance per unit mass flow of each component can be calculated with Equation 1 based on the first law of thermodynamics. The kinetic and potential energies are neglected, since they are very small compared to the heat transfer. [17]

(qi− qo) + (wi− wo) = ho− hi (1)

In the real cycle, the power cycle differs from the ideal cycle, since irreversibilities due to fluid friction and heat losses to the surroundings lowers the cycle efficiency. The irreversibilities mainly occur in the heat exchangers and in the pump as a re-sult from e.g. pressure drops and mechanical losses. The ratio of the real work is calculated using isentropic efficiencies according to Equation 2 and 3. [17]

ηt=

h3− h4

h3− h4s

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ηp=

h1− h2s

h1− h2

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2.1.1

Connection of ORC system

The connection of the ORC system is usually configured according to Figure 3, to accomplish both as high electricity production as possible and at the same time meet the requirements, for example a desired supply temperature to a district heating network, from the ORC condenser. The amount of heat ˙Qi that can enter the

system depends on these requirements. If the output temperature Toutput is the

same as the desired supply temperature Tsupply, all heat can run through the ORC

system. In cases where the output temperature from the ORC condenser is lower than the requirement, some heat needs to bypass the ORC system and thus be supplied directly to the condenser output in order to increase the condensers output temperature to the desired supply temperature. Even though a large heat input leads to large electricity production, a high output temperature will in turn lead to a higher condensation pressure. This will result in a smaller pressure difference over the turbine, if the turbine inlet state is maintained the same, and counteract the increased electricity production. To achieve as high electricity as possible, the choice of output temperature therefore needs to be optimized between heat input and pressure ratio over the turbine.

Figure 3: Illustration that shows how an ORC installation could look like. If the ORC system is connected at a heating plant, the heat source is usually a boiler and the cooling a district heating network. [18]

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2.1.2

Cycle efficiency

The thermal efficiency of the cycle is defined as the net amount of work divided by the amount of heat supplied, see Equation 4. Note that those definitions only are valid when assuming an adiabatic process.

ηth= wnet qin = wt− wpump qin (4) Work of the pump

wp = h1− h2 (5)

Turbine work:

wt= h3− h4 (6)

Heat input:

qin = h2− h3 (7)

2.2

District heating network

A district heating network (DHN) is a system for heat distribution where partial or entire towns are connected with a common underground pipe network. The heat is provided from a centralized heat production source, meaning that the users do not need to produce their own heat. The idea of the DHN is according to [19] ”to use local fuel or heat resources that would otherwise be wasted, in order to satisfy local customer demands for heating, by using a heat distribution network of pipes as a local market place”. Nowadays, the number of DHN all around the word is estimated to 8000. In Sweden alone over 500 are established. [19]

2.2.1

District heating networks in Sweden

In the DHNs in Sweden, there are large seasonal and daily variations of the heat load. The seasonal changes originate mainly from variation of the outdoor temper-ature between summer and winter in combination with the fact that tempertemper-atures inside buildings are more or less constant. The daily variations depend on the cus-tomer patterns due to individual and collective behaviours. [20] In Figure 4, the seasonal heat production variation is illustrated based on average values from 20 heating plants in Sweden.

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Figure 4: Average monthly heat production variation based on 20 Swedish heating plants. The heat production is large during winter when energy demand is high, and smaller during the warmer summer months.

In Figure 5, the average seasonal supply and return temperature variation is illus-trated based on 20 heating plants in Sweden.

Figure 5: Average monthly supply and return variation based on 20 Swedish heating plants.

2.3

Stodola’s Law of the Ellipse

The law of the ellipse was originally developed by professor Aurel Stodola, who dis-covered that the proportionality between inlet- and outlet pressure at the turbine and the mass flow through a multistage turbine, for given design parameters, had

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the shape of a segment of an ellipse, See Figure. 6 [11]

Figure 6: The proportionality between inlet pressure P01, outlet pressure P21 and mass

flow ˙m01 in a multistage turbine that has, in a Cartesian coordinate system, has the

shape of a segment of an ellipse. The figure originates from Wikimedia Commons, and is available via creative commons licensing [21].

The law is based on the mass flow coefficient Equation 8 and the elliptical propor-tionality stated in Equation 9. Where φ is mass flow coefficient, Pi is inlet total

pressure to the first stage, Po is exit static pressure from the last stage and Ti is

inlet temperature. φ = m˙ √ Ti Pi (8) φ ∝ s 1 − Po Pi 2 (9)

From 8 and 9 it follows that: ˙ m√Ti Pi = Ct s 1 − Po Pi 2 (10)

Where Ctis a unique constant for each turbine that needs to be obtained. The

equa-tions can also be restated as the ratio of off-design to design condiequa-tions, see equation 11. This eliminates the need for the proportionality constant. The subscript D refers to the design point for the turbine.

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φ φD = s 1 −  Po Pi 2 s 1 −  Po,D Pi,D 2 (11)

2.4

Turbine design

The design of a turbine is a complex process consisting of analysis on different levels. The turbine design is based on the characteristics of the cycle in which the turbine operates. Parameters like volume flow rate, pressure and temperature is during the turbine design process transferred to a turbine geometry adopted to various design constraints. The result is a turbine described by a lot of geometrical and other pa-rameters such as the number of stages and blades, blade shape, the rotational speed, pitch to chord ratio, and stagger angle.[22]

When designing the turbine one important parameter is to minimize the losses in the turbine, to get as high turbine efficiency as possible. The efficiency of the turbine is often defined as the ratio of real turbine work to isentropic work and the losses that occur are created by thermodynamic irreversibility or heat transfer, such as friction losses or leakage flows.

2.4.1

Turbine losses

The losses that occur in the turbine are commonly divided into three different cat-egories: profile losses, tip leakage losses and secondary losses. The losses that occur due to boundary layers on the blade surface are referred to as profile losses. Trailing edge losses, resulting from the pressure difference between the pressure and suction side of the blade, are also in many instance included in the category profile losses. These losses usually arise where the flow naturally moves from the high pressure side to the blade side with lower pressure. [23]

The second category, tip leakages losses, are caused because of the pressure differ-ence between the pressure and suction side of the blade, causing a flow between the rotor tip and the stationary end wall that will be mixed with the main flow. Since the leakage flow and the main flow have different angles and velocities this will result in losses. [23]

The secondary losses, also referred as endwall losses originate from the annulus wall boundary layers and their interaction with the blade rows. Since the boundary layer at the endwall separates in three dimensions, it creates a vortex resulting in a mixing between the main flow and the secondary flow. [23]

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2.5

Linear model for regression

Linear regression is a method for analyzing the relationship between two or more variables by fitting a linear set of basis functions, usually polynomial functions, that describes the dependence between them. The basic equations for the model is given by Equation 12, where X is the explanatory variable and Y the dependent variable. In this system of equations, the vector ¯k contains the coefficients of the polynomial, with k0 being the intercept.

¯

Y = X ¯k (12)

2.5.1

Least squares method

One of the most common methods for linear regression is the Least squares method. The least squares method minimizes the square difference between the actual data and the obtained model. For an over-determined system of equations, the error can be analytically minimized via the following equation.: [24]

¯

k = (XTX)−1XTY¯ (13)

The matrix X contains the full set of explanatory variables up to the Mth degree, and Y is a vector containing the corresponding dependant variables. [24]

X =      1 x1 . . . xM1 1 x2 . . . xM2 .. . ... . .. ... 1 xN . . . xMN      (14)

Using Equation 13, the optimal set of model coefficients is obtained. This method can be used for any functions which are well approximated by a polynomial of finite degree. However, this method is sensitive to noisy data, and extrapolation outside of the interval for which the function was created is not recommended. [24]

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3

Method

In the following chapter, the method for each research question is described and ex-plained. The first section contains an overall background to the programs that are used for obtaining the results and then continues to describe the work progress more in detail.

In Figure 7 below the programs that are used for obtaining the results are presented:

Figure 7: Illustration that shows which programs will be used to achieve the aim of the project.

Cycle-Tempo: Cycle-Tempo is a simulation program for thermodynamic cycle cal-culations. Input data is for example temperatures, flows, heat power and turbine efficiency, and output data is the expected electricity production from the ORC sys-tem. [25]

Againity’s turbine program (AGT): Againity’s in house developed turbine pro-gram is used to design investigate the performance of turbines. Input data is type of medium, mass flow and temperature and pressure before and after the turbine. The program then provides all necessary turbine data such as number of stages, turbine efficiency, axial forces, diameters, and angles of the turbine.

APES: Againity Performance Evaluation Software, APES, is a program that re-trieves logged data from Againity’s installed machines and runs thermodynamic calculations on detected steady state series. [26]

MATLAB: MATLAB is a programming platform that can be used to analyse data, develop algorithms and create models. The program has built-in math functions and can easily create plots and visualize data. In addition, the program provides high

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3.1

Compensations factors

The method for research question one, to obtain the compensations factors for off design performance, is illustrated in Figure 8.

Figure 8: Workflow for investigation of compensation factors. Part load scenarios between 100 % and 30 % with a step size of 10 % were investigated. The inlet pressure Pin for each part load scenario was obtained by using Equation 10. An iterative process

between AGT and Cycle Tempo was then performed to obtain the electricity production.

Firstly, the change of the condensation pressure during part load operation was investigated. Part load operation mostly occurs during the warmer summer months when the heat production at the district heating plants is decreasing, see Figure 4. As a result, the heat load in the ORC system is also decreasing, leading to less heat, ˙Qo, in the condenser is rejected to the return water from the DHN. Since the

mass flow ˙mDHN from the district heating network is decreasing as well, the output

temperature Toutput starts do decrease, as shown in Equation 15 , leading to a larger

pressure ratio over the turbine. However, since the DHN being less used during these part loads periods, the return temperature Treturn tends to increase, which slightly

counteracts the decrease in Toutput and the condensation pressure.

Toutput =

˙ Qo

cpm˙DHN

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The calculations showed that the output temperature decreased with 2 ◦C during autumn and spring, and 1 ◦C during summer. This investigation was conducted with data for ten different cases representing normal operating conditions for heat-ing plants in Sweden.

When the change in condensation temperature was investigated, the calculations of the partial load scenarios between 100 % (design point) and 30 %, with a step size of 10 %, were conducted using AGT and Cycle Tempo. The investigation was done for cases with a boiler temperature of 150 ◦C and 120 ◦C with a changing condensation temperature between 60 and 80 ◦C.

To obtain how much the electricity production decreased during off-design operation, Stodola’s law of the ellipse, Equation 10, was used to calculate the inlet pressure to the turbine. In this case, the medium was assumed to be a perfect gas and since the temperature will be more or less constant when the ORC system in connected to a boiler in a district heating plant, the influence of the temperature was neglected. The equation could then be rewritten as Equation 16, where the constant Ct was

calculated at the design point and used to calculate the inlet pressure, Pi to the

turbine at the part load scenarios. Po in the equation, is the outlet pressure from

the turbine and ˙mORC is the mass flow in the ORC system.

Ct= s ˙ m2 ORC P2 i − Po2 (16)

The output pressure and mass flow were obtained using Cycle Tempo. The inlet-and outlet pressure of the turbine for each partial load scenario were then used as input arguments in the AGT-program to calculate the efficiency of the turbine. The relative change in turbine efficiency, η0, was then calculated according to Equation 17 where ηt is the turbine efficiency at part load and ηt,D the turbine efficiency at

the design point.

η0 = ηt ηt,D

(17)

Lastly, the electricity production, ˙Wt was again calculated with Cycle Tempo using

the calculated inlet pressure and the turbine efficiency as input arguments. The compensation factor C for each part load scenario could then be calculated using Equation 18.

C = W˙tQ˙i,D ˙ Wt,DQ˙i

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The factor C can then be used to approximate losses in electricity production due to part load operation, by rewriting Equation 18 according to Equation 19.

˙ Wt= ˙ Qi ˙ Qi,D ˙ Wt,DC (19)

3.2

Output temperature

The workflow for research question two, to seek the optimal interval for the output temperature from the ORC condenser in relation to evaporation temperature/pressure, is shown in Figure 9. The goal was to develop a script that could find the best out-put temperature, Toutput, to maximize the annual electricity production and also

minimize the payback time. During the first step, the program Cycle-Tempo was used to examine how the thermal efficiency changed for different evaporation and condensation pressures. Statistically, the temperatures from the condenser have been in a range between 70-90 ◦C, but to ensure that the true optimum is found, temperatures between 60-100 ◦C were included in the study. Since the turbine effi-ciency is difficult to predict, this parameter was assumed to be constant for all cases. In reality however, the turbine efficiency tends to increase for larger systems with higher electricity production.

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Figure 9: Workflow for investigation of optimal interval of output temperature from the ORC condenser. For each output temperature from the ORC condenser Toutput, the

MATLAB script calculates the relative heat load, R, according to equation 20. Based on the relative heat load, the script tests possible choices of heat to the ORC system for the design point (see Figure 11). The script then chooses the best Toutput and heat to

ORC with respect to maximizing the annual electricity production and/or minimizing the payback time.

Data was then compiled for thermal efficiencies of the ORC system at a range of different pressures of the evaporator and condenser. To obtain a continuous func-tion of how the efficiency changed with respect to these parameters, a third degree polynomial was fitted using the least squares method. In Figure 10, the agreement between calculated data and the fitted function for thermal efficiency is shown. The Root Mean Square (RMS) error of the fitting is 7.86 ∗ 10−4.

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Figure 10: Agreement between calculated data and fitted function for thermal efficiency depending on evaporation and condensation pressure. The Root Mean Square (RMS) error of the fitting is 7.86 ∗ 10−4.

After obtaining the polynomial for the thermal efficiency, MATLAB was used to cal-culate the best Toutput with respect to maximizing the annual electricity production

and/or minimizing the payback time. Due to the heat input to the ORC system depending on how much lower the output temperature is than the supply tempera-ture to the district heating network (or other heat demanding process that require a specific temperature), see explanation in section 2.1.1, the output temperature has a large impact on the electricity production. The relative heat load, R, is calculated according to Equation 20.

R = Toutput− TReturn TSupply− TReturn

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During the calculations, the heat input to the ORC system also needs to take the monthly heat production variation at the heating plant into account. Statistics based on a range of Nordic heating plants show that most heat is produced during the cold months of December, January and February. Designing a turbine for optimal per-formance during those months only will cause the system to run on part load for the rest of the year, resulting in penalties due to bad compensation factors, as seen in Figure 11 (green line, 100 %). This will cause the overall electricity production throughout the year to be sub-optimal. Similarly, the green line representing the choice of 25 % of the maximum relative heat load clearly shows that designs which are based on months with low heat production might not result in partial loads, but will be unable to utilize the large heat production during winter. Thus, the best solution is often achieved by finding the right balance between part load operation and using most of heat production.

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Figure 11: Example of available heat throughout the year at a Nordic heating plant, in arbitrary units. Green lines represent a few possible choices for the design point based on maximum relative heat , R.

For each output temperature from the condenser, the annual electricity production was calculated in the MATLAB script. This was done by testing different design points for turbine operation, and calculating power output for each month. For months running at part load, the previously calculated compensation factors were used. In addition, to also find the optimum output temperature with respect to payback time, see Equation 21, the price to build the system was obtained using hardware prices, G, for the ORC system. The annual savings, a, were obtained by multiplying the average electricity spot price for each month with the monthly electricity production. The spot price used in the calculation was estimated based a economic forecast of the future electricity market carried out by Againity.

P ayback = G

a (21)

Finally, the results for the optimal temperatures were validated by comparing the calculated best output temperature, heat to ORC and annual electricity produc-tion, according to the MATLAB script, with corresponding calculations using Cycle Tempo and current calculation methods to ensure the correctness of the calculations.

3.3

Turbine design

To ensure a reasonable turbine design, an investigation of different design criteria, such as length of blade and load of the rotor, was carried out for different pressures ratios over the turbine, see Figure 12. The investigation was conducted by using

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the AGT program to find, for a fixed outlet pressure, the maximum possible inlet pressure for different modules and stages to fulfill the following criteria:

1. The load of the rotor, called Laufzahl, which is defined as ”peripheral velocity divided by the lossless gas velocity when expanding from static initial state to outlet pressure” [14], needs to be between 0.40 and 0.55 for turbines up to 110 kW electricity output and between 0.42 and 0.55 for larger turbines [14]. If the load is 0.55 or higher, a smaller module or less stages are required. 2. The length of the blades in the turbine must not be too long or to short.

Short blades result in both increased tip losses and secondary losses which corresponds to a low turbine efficiency. Long blades however, can become weak and cause vibrational problems.

The investigation of maximum inlet pressure was conducted for five different turbine (generator) sizes: 55 kW, 110 kW, 200 kW, 400 kW and 600 kW. For each turbine size and module, calculations with four, three and two stages were included in the study. Possible modules are T240, T375, T434, T583, T616, T708 and T810. The most common one is module T434. In all calculations an angular velocity of 3000 Revolutions Per Minute (RPM) was used in order to achieve the right frequency to the grid without using a gear box between the turbine and the generator.

Figure 12: Workflow for investigation of pressure ratios over the turbine that fulfill the design criteria. The investigation was performed for turbine sizes between 55 kW up to 600 kW were the outlet pressure of the turbine varied between 2 bar to 9 bar. Cycle Tempo was used to investigate the mass flow in the turbine which is used as input parameter in the AGT program to obtain different turbine designs.

3.4

ORC system performance

The investigation of the performance between measured data from an installed ORC system and theoretical calculations was conducted using APES. The program re-trieves historical logged data from an installed ORC system where it detects time

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series when the system is at approximately steady state (when the state in the sys-tem is constant in time). The steady state detection is applied on the evaporator heat flux, calculated from the water side of the evaporator. The method for data selection of the steady state criteria is developed by Cao and Rhinehart [28] which uses three filter factors λ1, λ2, λ3 which decide how through the criteria for steady

state should be. In addition to this, the program uses a factor called Rcrit which

sets the highest calculated value of R where the process should be considered steady. In this case the pre-defined values of these parameters were used since they already have been adjusted for the investigated ORC system. If another system will be analysed which not yet has been added into the system, these parameters need to be changed to fit the behavior of the investigated system. In Figure 13 the selected steady state series for for the investigated ORC system in this project are shown. Any steady state series less than five minutes where not included in this study.

Figure 13: Selected steady state series of the investigated ORC system. Rcrit = 2.5, λ1

=0.08, λ2 = 0.03, λ3 = 0.005

Furthermore, APES run thermodynamic calculations on the detected steady state se-ries, using fluid characteristics from Coolprop [29]. These results are summarized in an Excel file, containing data for each time step and average data for every detected steady state series. Since the aim was to analyze and compare how calculations agree with measured data, the following quantities were investigated:

1. The relation between turbine efficiency and inlet pressure 2. The relation between turbine efficiency and pressure ratio 3. The relation between mass flow and pressure ratio

4. The relation between thermal efficiency and heat load.

By analysing measured data and theoretical values from both AGT and Cycle Tempo, discrepancies between calculations and practical application can be found. This investigation will yield information about the validity of calculations carried out with AGT.

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4

Results

In this chapter the results for each research question are presented and visualised. The results are later discussed and analyzed in the chapter discussion.

4.1

Compensation factors

In Figure 14, the change in relative efficiency of the turbine is shown for part load scenarios between 100 % (design point) and 0 % for the investigated cases. Going from full load to lower values, the efficiency can be observed to increase at first. This, however, changes for partial loads lower than 50 %, where the efficiency is decreasing rapidly when moving towards lower loads. Due to high uncertainties for part load of less than 30%, the results in this range are not presented. Note that the relative change of the turbine efficiency also can behave differently depending on how highly loaded the turbine is at its design point (100%).

Figure 14: The Figure shows how the turbine efficiency is affected at part load operation. The blue dots are the calculated data points and the green line is the fitting using the least square method. Going from full load to lower loads, the turbine efficiency first increases, but after a load of 50% is starts to decrease rapidly.

The calculated compensation factors are visualised as blue dots in Figure 15. Error bars are based on one standard deviation. The factors both take the change in efficiency, inlet and outlet pressure of the turbine into account.

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Figure 15: The figure shows the calculated compensation factors during part load. The blue dots represent the calculated compensation factor for each part load scenario and the green line is a linear interpolation between neighboring points. The red error bars are based on one standard deviation.

4.2

Output temperature

Since the optimum condenser output temperature changes with operating conditions such as evaporation pressure and supply and return temperature to the DHN, Figure 16 presents the result for two specific cases. In case 1 the evaporation pressure is 19.8 bar and in case 2 the evaporation pressure is 13.4 bar. The supply and return temperature to the DHN of 90◦C and 50◦C, respectively. In this case, when maximizing the annual electricity production, the optimal output temperature from the ORC condenser is found to be 90◦C in case 1 and 82 ◦C in case 2.

Figure 16: Best output temperature from the condenser if the evaporation pressure is a) 19.8 bar and b) 13.4 bar when the supply- and return temperature to the district heating network is 90◦C and 50◦C, respectively.

With the same operating conditions as mentioned above, Figure 17 instead visualizes the best output temperature when minimizing the payback time. The best output

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temperature in case 1 was 78◦C and 75◦C for case 2. In Table 5 price per kWh, Toutput, heat to ORC, annual electricity production and payback can be seen for

both cases.

Figure 17: Payback time with respect to output temperature and heat ratio. The evapo-ration pressure is 19.8 bar and the supply and return temperature to the district heating network is 90◦C and 50◦C respectively.

Table 5: Optimal parameters with respect to annual electricity production payback time for case 1 and 2.

Case 1 Case 1 Case 2 Case 2 (Payback) (Payback) Price per kWh to build the ORC system 1.88 2.48 1.64 2.23

Toutput [◦C ] 90 82 78 75

Heat to ORC [kW] 6260 5008 3408 2391

Annual electricity production [MWh] 1517 923 1259 740

Payback time [Year] 3.34 4.41 2.96 4.10

In Figure 18 the best output temperatures for six different evaporation pressures are shown for different combinations of DHN supply and return temperatures with respect to annual electricity production. According to these calculations, the best output temperature for lower evaporation pressures/temperatures seems to be heav-ily dependent on the return temperature. This, however, seems to change at high evaporation pressures, where the best output temperature instead is more heavily depending on the supply temperature.

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Figure 18: Best output temperature from the ORC condenser, based on electricity pro-duction, for six different evaporation pressures, a) 19.8 bar, b) 16.4 bar, c) 13.4 bar, d) 10.9 bar, e) 8.7 bar, f ) 6.9 bar, for different combinations of supply and return tempera-tures to and from the DHN. From the graphs it can be noted that the output temperature is highly dependent on the evaporation pressure. The higher evaporation pressure, the higher is the best output temperature.

In Figure 19 the best condenser output temperature is shown when instead mini-mizing the payback time. While the overall trend is similar to the other results, the output temperature is lower in general, and the earlier smooth behaviour in the graphs is no longer seen.

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Figure 19: Best output temperature from the ORC condenser, based on payback time, for six different evaporation pressures, a) 19.8 bar, b) 16.4 bar, c) 13.4 bar, d) 10.9 bar, e) 8.7 bar, f ) 6.9 bar, for different combinations of supply and return temperatures to and from the DHN. The same trend as in Figure 29 can be seen here, that the output temperature is highly dependent on the evaporation pressure. However, the best output temperature is lower for each case and the smooth behavior in the graphs is no longer seen.

4.3

Turbine design

The results for research question three are presented in Figure 20 to 24 where the pressure ratio (Pi divided with Po) over the turbine with corresponding relative

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graphs fulfill the criteria explained in section 3.3: The load of the rotor is between 0.40 and 0.55 for turbines between 110 kW and between 0.42 and 0.55 for larger turbines. The blade lengths for each calculation has also been confirmed that they are not to short or to long. Note that all figures with label ”a” have a tempera-ture of 150◦C and figures with label ”b” have a temperature of 120◦C to the ORC evaporator. Furthermore, each shape represents a certain module and each color represents the number of stages.

In Figure 20 and 21 the maximum pressure ratio for a 55 kW and a 110 kW turbine has been analysed for two different modules (T375 and T434) with two, three and four stages respectively. It can be observed in both figures that the relative efficiency is in most cases higher when the temperature is 120◦C to the ORC evaporator than in the 150◦C case. An increased size of the turbine seems also to result in a higher possible pressure ratio.

Figure 20: Relative turbine efficiency at different pressure ratios for the investigated modules and stages for a 55 kW turbine. It can be observed that the larger modules or/and a increased number of stages increase the possible pressure ratio over the turbine. Furthermore, the relative turbine efficiency seems to decrease with higher pressure ratio.

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Figure 21: Relative turbine efficiency at different pressure ratios for the investigated modules and stages for a 110 kW turbine. The same trends as for the 55 kW turbine can also be seen here: larger modules or/and a increased number of stages increase the possible pressure ratio over the turbine and the relative turbine efficiency decrease with higher pressure ratio.

In Figure 22 the analysis was carried out for modules T583 and T434 for a 200 kW turbine. Similar trends as for the 55 kW and 110 kW turbine can also be seen hear.

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Figure 22: Relative turbine efficiency at different pressure ratios for the investigated modules and stages for a 200 kW turbine. The same trends as for the other investigated cases can be seen here as well: larger modules or/and a increased number of stages increase the possible pressure ratio over the turbine and the relative turbine efficiency decrease with higher pressure ratio.

Continuing to analyse the turbine efficiency and the pressure ratios in Figure 23 to 24 it can be observed that the pressure ratio changes greatly for most modules. This is however different from the turbines sizes between 50 and 200 kW, where the pressure ratio, for small modules, often is found to be similar across all calculations.

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Figure 23: Relative turbine efficiency at different pressure ratios for the investigated modules and stages for a 400 kW turbine. The same trends as for the other investigated cases can be seen here as well: larger modules or/and a increased number of stages increase the possible pressure ratio over the turbine and the relative turbine efficiency decrease with higher pressure ratio.

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Figure 24: Relative turbine efficiency at different pressure ratios for the investigated modules and stages for a 600 kW turbine.The same trends as for the other investigated cases can be seen here as well: larger modules or/and a increased number of stages increase the possible pressure ratio over the turbine and the relative turbine efficiency decrease with higher pressure ratio.

Overall, it is clear that larger modules and higher number of stages result in a larger pressure ratio over the turbine. As a general trend, however, the turbine efficiency tends to decrease with higher pressure ratio.

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4.4

ORC system performance

When analysing the measured and the theoretical data, some values in the figures seemed to be deviating. By examining the temperature difference over the turbine, see Figure 25, it was discovered that some of the values had a much higher difference between the inlet and outlet temperature of the turbine.

Figure 25: Actual measured temperature difference between inlet and outlet of the turbine for each time step.

At the left in Figure 26 to 28 the measured data for every time step is visualised and colored with respect to measured generator output. The theoretical calculated data for six different pressure ratios is also included in these figures as triangles. At the right side however, the same measured data for every time step is visualised but instead coloured depending on the temperature difference over the turbine.

In Figure 26 the turbine efficiency dependence on inlet pressure is shown. Since the actual turbine efficiency is confidential, values shown in the figures have been scaled and distorted. It can be seen that theoretical data and measured data agree well with each other for inlet pressures between 7.0 and 7.4 bar. At higher pressures, the theoretical turbine efficiencies and the electricity outputs seem to be slightly higher than the measured values. Important to note is that some values of the turbine efficiency deviates and have efficiencies between 0.8 and 1 in the figure. Reviewing the graph at the right side, most of these values are colored red meaning that these values have a temperature difference above 10 ◦C.

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Figure 26: Turbine efficiency dependence on inlet pressure for every time step. Note that the actual turbine efficiency is confidential, shown values have been scaled and distorted. The calculated data and measured data agree well with each other for inlet pressures between 7.0 and 7.4 bar. The deviating measured values are colored red in the Figure to the right meaning that these values have a temperature difference above 10◦C.

In Figure 27 the turbine efficiency dependence on pressure ratio is shown. The same observations regarding deviating values can also be seen here. Overall, the theoretical values seem to have good agreement with the measured data. At lower pressure ratios, the theoretical electricity production is estimated to be higher than the measured values.

Figure 27: Turbine efficiency dependence on pressure ratio for every time step. Note that the actual turbine efficiency is confidential, shown values have been scaled and distorted. Overall there is good agreement between calculated and measured data. At lower pressure ratios however, the electricity production is estimated to be higher than the measured values.

The dependence between mass flow and pressure ratio was also investigated as can be seen in Figure 28. The mass flow from the measured data is calculated based on the heat flux over the condenser. The theoretical values are calculated with AGT.

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Figure 28: Mass flow dependence on pressure ratio for every time step. The agreement between calculated and measured data is overall very good.

Lastly, the thermal efficiency was investigated according to Figure 29. The theoret-ical value at the design point was predicted to be 2.29 %. To the right in the figure, the average value for each time series can be seen.

Figure 29: Thermal efficiency dependence on heat load for every time step. To the left, thermal efficiency for every time step is shown, to the right the average value for each time series can be seen. The predicted theoretical value of the thermal efficiency at the design point was predicted to 2.29 %.

In Figure 30 and 31 the same quantities as in Figure 26 and 27 can be seen, but with the difference that the values in the graphs are for average data for each time series.

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Figure 30: Turbine efficiency dependence on inlet pressure based on average data for every time series. Note that the actual turbine efficiency is confidential, shown values have been scaled and distorted.

Figure 31: Turbine efficiency dependence on pressure ratio based on average data for every time series. Note that the actual turbine efficiency is confidential, shown values have been scaled and distorted.

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5

Discussion

In this section, the result for each research question are discussed and analysed both with respect to error sources and reliability of the projects outcome.

The result for the calculated compensation factors show, according to Figure 14 and Figure 15, that the electricity production is decreasing more rapidly at lower load. This is however expected since the turbine efficiency at loads between 80 % and 60 % first increases, which to some extent counteracts the decrease in heat to the ORC system. After part load scenarios lower than 50 % the turbine efficiency is decreas-ing rapidly down to zero, resultdecreas-ing in lower compensations factors. When analysdecreas-ing the red error bars, it can be noted that the error tends to be larger on lower loads. This originates from the calculated turbine efficiency which differed more between the investigated cases at lower loads. The reason for this may be that the turbine having different loads at its design point, resulting in different behaviors during part load operation.

As mentioned in section 3.1, the compensation factors also take the change in con-densation pressure during part load into account. The calculation, based on ten heating plants, showed that the output temperature from the ORC condenser de-creased on average with 2 ◦C during autumn and spring and 1◦C during summer. This is however heavily case dependent and for some of the investigated cases, the output temperature could decrease up to 6◦C. Considering that this effect mostly occurs during summer months when electricity production is at its lowest, this would barely effect the result when using the compensation factors to estimate the annual electricity production with the ORC system. Furthermore, since input data such as heat production, supply and return temperatures always is based on historical data, there is a substantial source of error in these values. The approximation of the compensation factors, on the other hand, has the largest errors at lower loads, when electricity production is at its lowest. Therefore, the argument can be made that the calculated function does not introduce errors which have substantial effect on the overall results, and the compensation factors are sufficient for calculation of the estimated electricity production. The presented values were calculated for a boiler temperature ranging from 120 to 150 ◦C, and calculations for heating plants with different temperatures may therefore have larger errors. These temperatures however, represent the conditions for most of the heating plants in Sweden.

In the second research question, the best ORC condenser output temperature was investigated both with respect to annual electricity production and payback time. Even if the output temperature is not constant in reality, it is a simple and quick method to estimate the annual electricity production by finding a suitable temper-ature to the turbine design point, where the best combination of heat through the ORC system and pressure ratio is obtained. At months when the turbine works on part load, the obtained compensation factors from the first research question were used to estimate the electricity production. Analysing Figure 18, the best output

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temperature is, as expected, highly dependent on the evaporation pressure. The higher the evaporation pressure, the higher the output temperature. In Figure 19 a similar result can be observed when instead finding the best output temperature with respect to payback time. The overall output temperature is however lower for each case. This is to be expected, since if not take the price into account, a higher amount of heat into the system is to prefer to increase the electricity production. To accommodate the increase in heat, however, the flow in the system increase as well, and more heat exchangers are needed, leading to a higher hardware price for the system. This in turn results in lower output temperature when optimizing with respect to payback time, since this will achieve a higher thermal efficiency of the system and thus lesser heat into the system is needed.

In the MATLAB program, a number of assumptions are made, each of which can lead to a different in the predicted and actual electricity production. Firstly, the program is case dependent, and data over available heat is therefore based on historical data, which can vary between different years. Furthermore, if optimization with respect to payback time is carried out, the payback time is calculated based on an estimate of the future electricity market. This is a rather coarse approximation, since the electricity market has been volatile in recent years. According to a study conducted by Svenska Kraftn¨at [30] regarding the future electricity price, the numbers of hours with both low (< 5 EUR/MWh) and high (> 80 EUR/MWh) electricity prices will most likely increase as a result of a greater share of intermittent energy sources in the energy system. A stronger interconnection with the continent and the UK will also contribute to hours with higher future prices in the Nordic region.

Lastly, the cycle efficiency is estimated via a function, according to Figure 10, based on accurate cycle calculations. While this decreases the time and computational de-mand for calculations, it also introduces a small error in the final results, of roughly ±0.1 % when estimating thermal efficiency. This program should therefore be used to get a good overview of the viable options for a given case, and the optimal solu-tion should always be confirmed with an accurate cycle simulasolu-tion.

In Figures 20 to 24 the maximum pressure ratio over the turbine is presented for modules between T375 and T616 from two up to four stages. As mentioned in sec-tion 4.4, the turbine efficiency tends to decrease with higher pressure ratios. This trend is a result of the change in volume flow and blade length. By using a larger module, a larger pressure ratio over the turbine is possible, and the blade length is usually shorter, due to the increase in flow area. This in turn decreases the heat flow through the system to generate the requested electricity. As a result, the volume flow into the turbine decreases, leading to shorter blades and since shorter blades contributes to larger tip and secondary losses, the turbine efficiency decreases. The same reasoning can be done with increased number of stages due to the ability to obtain higher pressure ratio over the turbine.

For small modules, the pressure ratio is often found to be similar across all calcula-tions for the different outlet pressure from the turbine. For larger modules, on the other hand, great changes in the pressure ratio can be observed. This behaviour is

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due to the calculations for larger module quickly approaching the maximum input pressure, after which only the output pressure can change, leading to a decrease in the ratio. For smaller modules, the maximum value for the input pressure is never reached, and the pressure ratio thus stays the same over all investigated output pressures.

Based on the calculations for research question three, the overall conclusion is that module T434 is good to use for all conditions. By only changing the number of stages depending on wanted electricity production, a good turbine design can be obtained for any of of the investigated system size.

Comparison between calculations and measured data for an installed ORC system, investigated in the last research question, showed that the agreement between the data sets for most cases were in agreement with each other. At lower inlet pressures and at smaller pressure ratios, the calculated turbine electricity output seemed to be slightly higher than for the measured data points. However, some values in the figures highly deviated as a result from a high temperature difference across the tur-bine. Possible reasons may be that the turbine was in a start-up mode and therefore cold, causing the large temperature difference. However, this is considered unlikely because the steady state functionality of APES should have sorted out these values. A more reasonable explanation is that this derives from an error of measurement due to equipment malfunction. A similar study investigating the performance of an ORC system, had issues with faulty sensors as well, resulting in unrealistic turbine efficiencies above 100% [31]. In that case this was caused from a failing pressure sensor at stage four (output pressure from the turbine). Most likely, the deviations observed in this study derived from an error in the sensors as well.

By analysing Figure 29, it can be concluded that the theoretical values of the ther-mal efficiency agree well with the measured data at full load. At lower loads, the thermal efficiency appears to be declining more heavily than expected. Comparison with the results from research question one, when analysing compensations factors during part load operation, the thermal efficiency should not decrease that heavily already after 85 % load. Considering that the part load investigation was performed for heat source temperatures at 150◦C and 120◦C respectively, but the investigated system only had a temperature of 105◦C from the heat source, this could be the reason to the rapidly decreasing trend. Since just a small decrease in the tempera-ture will stand for a large percentage of the total temperatempera-ture difference, this will have great effect on the electricity production. Furthermore, when the temperature difference decreases, the pump in the system will try to compensate by increasing the mass flow in the system. This will in turn result in a higher electricity demand for the pump.

Since the comparison only has been carried out for one ORC-system with an electric-ity output of 50 kW, it is important to continue the investigation of the agreement also for larger systems, in order to verify both the compensation factors and to ensure that calculated values agrees with the the actual performance of the ORC systems.

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6

Conclusions

Estimating electricity output during part load operation of a turbine is an impor-tant but time consuming task. By using the calculated compensation factors, the process to investigate potential electricity production at an early stage will be much more time efficient. Furthermore, using the developed MATLAB script to calculate the optimum interval of output temperature will also speed up the workflow, by estimating which temperature that will be best suited for the design point. In the two investigated cases (case 1 and case 2) the best output temperature was 90 and 82◦C when maximising the electricity production and 78 and 75 ◦C when minimiz-ing payback time. The presented Figures 18 and 19 can also act as rules of thumb to approximate in what interval the temperature should be within.

Investigation of a wide range of different pressures for modules with varying num-ber of stages allows to find the most viable design point to ensure high electricity production. The approach taken in this study can quickly and easily find such point for the given set of conditions at a potential heating plant preparing to upgrade to a CHP plant. Based on the calculation, module T434 is good to use for almost all conditions since a good turbine design could be archived by only change the number of stages. Furthermore, comparison between theoretical findings and actual mea-sured data showed that results are in reasonable agreement with the performance of the measured ORC system. Since the comparison however only has been carried out for a small ORC system, investigation of larger systems needs to be analysed as well in order to verify that the calculated values agree with actual performance. Since narrowing down the range of possible temperatures and pressures can shorten the time scale needed for full-scale investigation of the potential electricity produc-tion, a tool like this can greatly effect computational efficiency and time demand of case calculations.

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7

Outlook

The projects aim to improve the prediction of electricity production under varying loads was achieved, but there are still further improvements that could be imple-mented. The script that was used to investigate the best output temperature from the ORC condenser is for example using a function for thermal efficiency based on evaporation and condensation pressure. To increase the accuracy, Coolprop could be implemented to be able to perform cycle calculation directly in MATLAB. Imple-menting the result from research question three to ensure that the pressure ratio in the cycle is in agreement what is possible for the turbine, could also be a possibility in the future.

In the last research question, when measured data was compared to calculated data, both the agreement between thermal efficiency and turbine efficiency were found to be in good agreement with each other. Since this comparison only has been made for one ORC system with an electricity output of maximum 50 kW, further research is needed for larger ORC systems as well.

References

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