Grant Agreement No: 680447
Project acronym: MODER
Project title: Mobilization of innovative design tools for refurbishing
of buildings at district level
Funding scheme: Innovation Action
Starting date of project: 1st September 2015
Duration: 36 months
D4.3 – Energy system component unit model library
Due date of deliverable: February 28, 2017
Actual submission date:
WP 4
Task 4.3
Leader: Siemens AG
Leader: Siemens AG
Dissemination Level
PU/CO Public / Confidential, only for members of the consortium (including the PU
Commission Services)
Table of Contents
Table of Contents............................................................................................................................ 1
1
Introduction ............................................................................................................................. 3
1.1
Publishable summary ...................................................................................................... 3
1.2
Purpose and target group ................................................................................................ 3
1.3
Contribution of partners ................................................................................................... 3
1.4
Relation to other tasks/deliverables ................................................................................. 3
1.5
Terminology and definitions ............................................................................................. 3
2
Energy system superstructure ................................................................................................. 6
2.1
Energy demands and available input energy forms ......................................................... 6
2.2
Candidates for energy conversion and storage units ....................................................... 6
2.3
Energy system superstructure ......................................................................................... 7
3
Model library ........................................................................................................................... 8
3.1
Overview ......................................................................................................................... 8
3.2
Generic energy conversion unit model............................................................................. 8
3.3
Generic energy storage unit model .................................................................................. 9
3.4
Example models ............................................................................................................ 10
3.4.1 Renewables ............................................................................................................... 10
3.4.2 Heat pumps and compression chillers ....................................................................... 11
3.4.3 Absorption chillers ..................................................................................................... 12
3.4.4 Gas turbines and turbine inlet air cooling ................................................................... 15
3.4.5 Ice storages ............................................................................................................... 21
3.5
Economic and regulatory boundary conditions .............................................................. 23
4
Conclusion ............................................................................................................................ 25
5
References............................................................................................................................ 26
Appendix ....................................................................................................................................... 30
A. Model parameters ............................................................................................................. 30
D4.3 Energy system component units model library
1
History
Version
1.1
Description
Draft for comments, confidential
Lead author
Sebastian Thiem
1.2
Final version, public
Sebastian Thiem
Date
January
13, 2017
April 7,
2017
Acknowledgements
The work presented in this document has been conducted in the context of Horizon 2020 programme of the European
community project MODER (n° 680447). MODER is a 36-month project that started in September 2015 and is funded by
the European Commission as well as by the industrial and research partners. Their support is gratefully appreciated.
The partners in the project are:










Sweco Finland Ltd. (Finland)
VTT Technical Research Centre of Finland Ltd.(Finland)
Fraunhofer Gesellschaft zur Forderung der Angewandten Forschung EV - Fraunhofer Institute
for Building Physics IBP (Germany)
Siemens AG (Germany)
REM PRO SIA (Latvia)
Stichtung W/E Adviseurs Duurzaam Bouwen - W/E Consultants Sustainable Building (The
Netherlands)
Ertex Solartechnik GmbH (Austria)
Gradbeni Institut, ZRMK DOO – GI ZRMK (Slovenia)
Finnenergia Oy (Finland)
Lokalna Energetska Agencija Gorenske Javni Zavod - LEAG (Slovenia).
D4.3 Energy system component units model library
2
1 Introduction
1.1 Publishable summary
The objective of Task 4.3 was to develop a structure for the description of energy conversion and
storage units and to set up a model library.
Generic models for both energy conversion units and energy storage units were developed. The
models were described in a way to be used by the energy system design method in Task 4.4.
Furthermore, model parameters for the energy system components were determined using one of
the following three methods:



Models were determined based on published data
A physical model was developed and simplified to determine the parameters
The component was experimentally investigated
The generic models along with the model parameters constitute the model library. The model
parameters were summarized in the appendix.
1.2 Purpose and target group
The energy system component unit model library is intended to serve as the foundation and data
basis for the advanced holistic energy system design method.
The target group of Task 4.3 was the MODER consortium.
1.3 Contribution of partners
The work was organized and reported by Siemens AG. The following experts contributed to
developing the model library and determining the model parameters:







Vladimir Danov
Michael Metzger
Jochen Schäfer
Ludwig Bär
Dieter Most
Florian Reißner
Sebastian Thiem
1.4 Relation to other tasks/deliverables
This work has a relation to Task 4.4. In Task 4.4, an advanced method for holistic energy system
design will be developed.
1.5 Terminology and definitions
Table 1.1 shows the abbreviations used in this text. The symbols were tabulated in Table 1.2 and
Table 1.3 below.
D4.3 Energy system component units model library
3
Table 1.1 – Abbreviations.
Abbreviation
AC
AG
CC
CHC
CWS
EB
ECES
GB
GT
HP
HVAC
HWS
ICE
ISO
ITES
LeadAcid
LiIon
PV
REFPROP
rHP
SGT
SQP
ST
TIAC
WT
Description
Absorption chiller
Aktiengesellschaft (Public holding company)
Compression chiller
Combined heat and cooling heat pump
Chilled water storage
Electric boiler
Electrochemical energy storage
Gas boiler
Gas turbine CHP
Heat pump
Heating, ventilation and air-conditioning
Hot water storage
Internal combustion engine CHP
International Organization of Standardization
Default (nominal) gas turbine conditions
Ice thermal energy storage
Lead-acid battery
Lithium-ion battery
Photovoltaic
NIST Reference Fluid Thermodynamic and Transport Properties Database
Reversible heat pump
Siemens Gas Turbine
Sequential quadratic programming
Steam turbine including entire steam cycle
Turbine inlet air cooling
Wind turbine
Table 1.2 – Symbols (Latin).
Symbol
Unit
[m²]
[€]
specific
[J/kg/K]
[J/kg/K]
specific
[-]
[J]
[J]
[-]
specific
[W/m²]
[J/kg]
[J/kg]
[W/m²/K]
[%/s]
[kg]
[kg/s]
[-]
Description
Heat transfer surface area
Costs
Coefficient
Specific heat capacity at constant pressure
Specific heat capacity at constant volume
Nominal capacity
Coefficient of performance
Energy contained in energy storage
Exergy
Energy efficiency ratio
Specific function
Global horizontal irradiance
Specific enthalpy
Specific enthalpy of phase change
Heat transfer coefficient
Specific self-discharge rate
Mass
Mass flow rate
Online status of an energy conversion unit
D4.3 Energy system component units model library
4
[W]
[Pa]
[W]
[J/kg]
[J/kg/K]
[%/s]
[€/W/start]
[K]
[s]
[°C]
[K]
[°C]
[K]
[°C]
[-]
[m³/s]
[m/s]
[m³/kg]
[J/kg]
[-]
[-]
Power flow
Pressure
Heat flow rate
Specific heat
Gas constant
Ramping constraint
Specific start-up costs of an energy conversion unit
(Dry-bulb) temperature
Time
(Dry-bulb) temperature
Dew-point temperature
Unit
[1/K]
[-]
[-]
[-]
[-]
[-]
[-]
[-]
[kg/m³]
[-]
Description
PV temperature coefficient
Heat exchanger effectiveness
Heat ratio
Efficiency
Heat capacity ratio
Grade
Mass concentration
Pressure ratio
Density
Relative humidity
Wet-bulb temperature
Part-load ratio
Volumetric flow rate
Speed
Specific volume
Specific work
Humidity ratio
Boolean variable
Table 1.3 – Symbols (Greek).
Symbol
D4.3 Energy system component units model library
5
2 Energy system superstructure
2.1 Energy demands and available input energy forms
Buildings within a city district demand different forms of energy:




Electricity
Heating
Hot water
Cooling
Furthermore, electricity may be sold at the wholesale electricity market or may be sold at
designated feed-in tariffs. Some conversion units also emit CO2 and other emissions.
The city district is commonly connected to the power grid, a natural gas grid, and may also be
connected to a district heating or district cooling grid. Solar irradiance and wind are available free
of charge.
2.2 Candidates for energy conversion and storage units
Based on the available input energy forms, candidates for supplying the previously mentioned
energy demands were identified. These were categorized in the following two categories:


Renewable energy conversion units
1. Photovoltaic (PV)
2. Wind turbines (WT)
Energy conversion units
1. Internal combustion engine CHP plant (ICE)
2. Gas turbine CHP plant, simple cycle (GT
3. Gas turbine CHP plant, combined cycle (GT + ST)
4. Gas boiler (GB)
5. Electric boiler (EB)
6. Heat pump (HP)
7. Heat pump that simultaneously supplies both heat and cold (CHC)
8. Reversible heat pump (rHP)
9. Absorption chiller (AC)
10. Compression chiller (CC)
Furthermore, energy storages enhance the flexibility of the energy supply system and can help
increasing the share of energy supplied by renewables or to lower plant costs by peak shaving.

Energy storage units
1. Lead-acid battery (LeadAcid)
2. Lithium-ion battery (LiIon)
3. Hot water storage (HWS)
4. Chilled water storage (CWS)
5. Ice thermal energy storage (ITES)
The lists contain typical technologies that are used for the energy supply system of city districts;
either on a household-level or on district-level.
D4.3 Energy system component units model library
6
2.3 Energy system superstructure
The energy system components were arranged in a technical superstructure (see Figure 2.1). The
superstructure is a structure that describes the energy system with the maximum set of
technologies. All components are connected to each other in physically-feasible ways. The holistic
energy system design method in Deliverable D4.4 shall be able to select those technologies that
are most attractive for a given use case.
Electricity (AC)
Exhaust gas (500 – 600 °C)
Glycol-water (-10 - 0 °C)
Electricity sale
Steam (120 – 170 °C)
Chilled water (4 - 12 °C)
Fuel (e.g., NG)
Hot water (80 – 90 °C)
Ambient air
Warm air (30 – 50 °C)
Energy converter
Energy storage
Carbon dioxide
Figure 2.1 – Technical superstructure.
Electricity could be supplied by renewable energy technologies, such as photovoltaic and wind
turbines. Cogeneration systems, such as gas turbine (simple cycle or combined cycle) or
combustion engine CHP plants, could also supply electricity, but also supply heat at the same time.
Other heating options are gas boilers, electric boilers (resistive heaters) and heat pumps.
Absorption chillers, compression chillers and reversible heat pumps provide chilled water for
cooling purposes. Electricity can be conveniently stored in electrochemical energy storages, such
as lead-acid batteries and lithium-ion batteries. Thermal energy storages include hot water
storages, chilled water storages and ice storages.
D4.3 Energy system component units model library
7
3 Model library
3.1 Overview
A generic model for energy conversion units (Section 3.2) and a generic model for energy storage
units (Section 3.3) were developed. The generic models contain several parameters that were
determined for each of the energy system components. The model parameters were tabulated in
Appendix A.
3.2 Generic energy conversion unit model
A generic energy conversion unit is shown in Figure 3.1 (a). An energy conversion unit ( ) may
convert multiple input power flows (
) to multiple output power flows (
). An output power
flow is coupled to an input power flow by its efficiency:
(3.1)
Here, the index
denotes a discrete time step.
(a)
Energy conversion unit
Pin , j ,1
Pout, j ,1
…
…
Pin, j,m
Pout, j ,1,k
(Potentially) feasible region
Cap j  umax, j Tamb 
Cap j
su j
(c)
Pout, j ,1
Cap j
Pout, j ,1,k
Cap j  umin, j Tamb 
Tamb ,k
Tamb
…
…
(b)
Pout, j,n
ηj
Cap j
(Potentially) feasible region
Cap j  rj
Cap j  rj
tk
tk 1
t
Figure 3.1 – Generic energy conversion unit model.
The first output power flow (
) was defined as the output power flow that determines the
capacity (
) of the energy conversion unit ( ). Hence, we can define a part-load ratio ( ) as:
(3.2)
D4.3 Energy system component units model library
8
The part-load ratio may be constrained by minimum (
) and maximum (
) values. The
energy conversion unit can only operate within these limits (see Figure 3.1 (b)). A new Boolean
variable (
) is used to describe the operation status of the energy conversion units. Now
we can write:
(3.3)
Due to material constraints and due to the thermal inertia of components of an energy conversion
unit, maximum positive ( ) and negative ( ) ramping constraints could further constrain the
feasible operation of the conversion unit (see Figure 3.1 (c)):
(3.4)
Equation (3.1) – Equation (3.4) are the basic equations for the description of energy conversion
units. The parameters (e.g.,
) must be determined for each conversion unit ( ) and if
applicable also for each time step ( ). Table A.3 - Table A.10 list the model parameters for the
energy conversion units considered in this project.
3.3 Generic energy storage unit model
A generic energy storage unit is shown in Figure 3.2 (a). An energy storage ( ) may be charged
(
) or discharged (
). Furthermore, an energy storage could discharge itself (
) with
time.
(a)
(b)
Cap j
Ej
Energy storage
Cap j  rj
Cap j
E j ,k
E j ,k 1
E j ,k
Cap j  rj
ch , j
dch, j
0
0
l j E j ,k
Pch , j ,k
Pdch, j ,k
tk
tk 1
t
Feasible region
Figure 3.2 – Generic energy storage unit model.
The change of the energy storage energy content (
could be described as follows:
) across a time step (
)
(3.5)
The energy that can be contained within the energy storage is constrained by (see Figure 3.2 (b)):
D4.3 Energy system component units model library
9
(3.6)
Furthermore, the net charging (
3.2 (b)):
) and discharging (
) rate can be limited (see also Figure
(3.7)
Equation (3.5) – Equation (3.7) are the basic equations for the description of energy storage units.
Once again, the parameters (e.g., ) were determined for each energy storage unit ( ) and if
applicable also for each time step ( ). Table A.11 - Table A.15 list the model parameters for the
energy storage units considered in this project.
3.4 Example models
The model parameters for the individual components were determined using one of the following
three ways:



(M1) Datasheet or literature: Models were determined based on published data
(M2) Physical model: A physical model was developed and simplified to determine the
parameters
(M3) Empirical model: The component was experimentally investigated
The models for five example energy system components are briefly introduced below:





Fluctuating renewable energies (M1): Section 3.4.1
Heat pumps and compression chillers (M1, M3): Section 3.4.2
Absorption chiller (M1, M2): Section 3.4.3
Gas turbine including turbine inlet air cooling (M2, M3): Section 3.4.4
Ice storage (M3): Section 3.4.5
3.4.1 Renewables
The renewable energy conversion units were modelled based on published information available
on datasheets and in literature.
The potential power output ( ) of renewable energy conversion units is computed by multiplying its
relative power output ( ) with the capacity (
) of the unit ( ).
(3.8)
The relative power output describes the potential of the renewable energy source. For photovoltaic
panels, it could be modelled as:
(3.9)
D4.3 Energy system component units model library
10
with the parameter ( r
) [1].
denotes the ambient temperature at a time step
( ). Wind turbines have a distinct output characteristic that depends on the wind speed. It was
modelled as piecewise-defined function [2–4]:
r
(3.10)
r
In Equation (3.10), the following parameters were distinguished:



Cut-in speed (
Rated speed ( r
Furling wind speed (
s)
s)
s)
Further model parameters of the two renewable energy conversion units were tabulated in the
appendix in Table A.1 and Table A.2.
3.4.2 Heat pumps and compression chillers
The models for the heat pumps and compression chillers were derived from both datasheets and
based on experiments. The process & instrumentation diagram of a generic heat pump is shown in
Figure 3.3 (a). Figure 3.3 (a) depicts the thermodynamic cycle (1 - 4). The refrigerant (1) is
compressed (2), then condensed which releases heat (3) and expanded (4). At low temperatures it
can now evaporate back to the initial state (1). The energy for the evaporation is provided by heat
transferred to the refrigerant [5].
(b)
(a)
ln p
Q cond
Critical point
2
Condenser
Liquid
Compressor
Liquid
Pel
3
pcond
3
2
 1
 0
  const.
Expansion
valve
pevap
1
4
Vapor
qcond
4
Vapor
wt
qevap
Evaporator
Q evap
1
h3 h4
h1
h2
h
Figure 3.3 – Heat pump: (a) Process & instrumentation diagram, (b) Thermodynamic cycle [5].
D4.3 Energy system component units model library
11
The efficiency of heat pumps is also called coefficient of performance (
[5]:
). It is defined as follows
(3.11)
is the heat flow rate transferred at the condenser and
is the electric power input to the
compressor. The efficiency of compression chillers is described by its energy efficiency ratio (
)
[5]:
(3.12)
is the heat flow rate transferred to the refrigerant within the evaporator. The maximum
coefficient of performance (
) and energy efficiency ratio (
) is given for a Carnot
cycle as [5]:
(3.13)
(3.14)
Equation (3.13) and Equation (3.14) show that the maximum efficiency for air-coupled heat pumps
or compression chillers (e.g., air-water heat pumps) depends on the ambient temperature.
Gordon and Ng derived a quasi steady-state model for compression chillers based on the first and
second law of thermodynamics [6–8]. They relate
to easily measurable temperatures (
,
) and the evaporator heat flow rate (
):
(3.15)
is the temperature of the cooling water flow into the condenser.
is the temperature of
the chilled water flow into the evaporator. The equation can be reformulated for heat pumps. Based
on this model, the technical performance of heat pumps and compression chillers in quasi steadystate can be described fairly well [9,10].
3.4.3 Absorption chillers
Absorption chillers (AC) replace the electrically-driv n o pr ssor by a “th r al o pr ssor” (s
Figure 3.4 for an ammonia-water absorption chiller).
D4.3 Energy system component units model library
12
NH3 vapor
ref
 1
“Thermal compressor”
5
Q gen
Q cond
Generator
Condenser
NH3
liquid
ref
 1
4
Weak
H2O / NH3
solution
w 
6
Recuperator
Pel,pump
Refrigerant
expansion
valve
Solution
expansion
valve
7
Evaporator
Q evap
3
8
1
Absorber
NH3 vapor
ref
 1
Q abs
Solution
pump
2 Rich
H2O / NH3
solution
r 
Figure 3.4 – Absorption chiller: Process & instrumentation diagram.
Similar to the compression chiller, AC operate on two pressure levels, evaporator (
) and
condenser (
) pressure, see also Figure 3.5. In the generator, rich ( ) solution of ammonia
(NH3) in water (H2O) (3) is evaporated driven by the generator heat flow rate (
). A weak ( )
solution (4) with less ammonia leaves the generator. Ideally, the vapor leaving the generator (5) is
pure ammonia (
); in reality, this case is only reached by rectification for ammonia water
solutions. Other AC operating with water and lithium bromide (LiBr) achieve this state without
rectification. However, since H2O-LiBr absorption chillers use the refrigerant water, cooling supply
temperatures below 0 °C cannot be reached. Thus, this technology is not of use for ice storages.
Analogously to compression chillers, the refrigerant vapor is condensed (6) and afterwards
expanded to evaporator pressure levels (
) (7). At evaporation temperature, heat is transferred
to the refrigerant to evaporate it (8). The weak solution leaving the generator (4) flows through the
recuperator transferring heat to the rich solution (3) before it enters the generator. In the solution
expansion valve, the weak solution is expanded to evaporator pressure. The refrigerant vapor (8)
is absorbed by the weak solution (1). A solution pump pumps the rich solution (2) from the
absorb r through th r up rator to th g n rator. Th “th r al o pr ssor” is abl to in r as
the pressure of the refrigerant by exergy that is supplied to the absorption chiller along with
.
Besides small electric power for the solution pump (
) and other auxiliary equipment, AC are
driven by thermal energy [5].
D4.3 Energy system component units model library
13
ln p

mNH 3
mNH 3  mH 2O
pcond
pevap 7 8
1
1
T Tevap
ref  1  r  w

5
3
6
2
1
Tcond
4
1
1
1
T1 1 T4
T3
Figure 3.5 – Absorption chiller: Thermodynamic cycle.
The grade ( ) is defined as the exergy ratio of evaporator exergy rate (
rate (
) [11]:
) and generator exergy
(3.16)
Another ratio that is commonly used to describe absorption chillers is the heat ratio ( ) [5]:
(3.17)
The maximum heat ratio can be determined for a Carnot cycle with
as follows [5]:
(3.18)
The energy efficiency ratio, on the other hand, is another parameter that considers both generator
heat flow rate (
) and electric power drawn by the solution pump (
) as required inputs:
(3.19)
D4.3 Energy system component units model library
14
A physical model for one-stage ammonia-water absorption chillers was developed. The physical
model was based on a dimensioning approach outlined by v. Cube [11]. Properties of the
ammonia-water mixture were computed using the software REFPROP1 from the National Institute
of Standards and Technology. Utilizing the physical model, the coefficients of a steady-state model
for the heat ratio ( ) derived by Gordon and Ng [12],
(3.20)
were determined. Hence, the physical model could be simplified to an accurate but more useful
model.
3.4.4 Gas turbines and turbine inlet air cooling
Gas turbines (GT) convert the chemical energy of a natural gas-air mixture through combustion to
electrical energy and hot exhaust gases.
Figure 3.6 (a) shows a process and instrumentation diagram of a gas turbine. The compressor
compresses inlet air (1) with a certain pressure ratio. The temperature is also increased. The hot
and compressed air (2) enters the combustion chamber, fuel is injected and the gas-air mixture is
ignited. The temperature of the gas mixture increases. This gas (3) enters the turbine that expands
the mixture to near-atmospheric pressures (4). The gas mixture produces work on the shaft in the
turbine stage, which is partly used to power the compressor and partly is available as net electrical
power output of the GT [13].
The thermodynamic cycle of a simple cycle gas turbine is shown in Figure 3.6 (b). The compressor
requires more work ( ) than in the ideal, isentropic case (
). Furthermore, the power output of
the turbine is also smaller than in the isentropic case (
). In addition to this, a pressure drop
across the combustor occurs [14].
1
REFPROP: Reference Fluid Thermodynamic and Transport Properties Database. Accessible at URL:
http://www.nist.gov/srd/nist23.cfm.
D4.3 Energy system component units model library
15
(a)
(b)
Q comb
Fuel
p = const.
h
3
Combustor
2
3
Pel
wt
wt,s
2
2s
Compressor
4
Turbine
wc
wc, s
1
4
4s
p = const.
1
Air
Exhaust gas
s
Figure 3.6 – Gas turbine: a) Process and instrumentation diagram, b) Ideal (dashed line) and real (full line)
thermodynamic cycle in a enthalpy ( )-entropy ( ) diagram [5,13].
The main advantages of gas turbines over other conventional power plants are:



Fast start-up and load-changing rate due to lightweight design
High efficiency in combined cycle due to high exhaust temperatures that can be used for
steam cycles
Lower specific emissions due to fewer impurities in natural gas compared to coal and higher
H/C (hydrogen/carbon) ratio
Gas turbines, however, also have certain drawbacks:


High variable costs due to high natural gas prices in many regions of the world and high
specific invest
Lower efficiencies, when used in simple cycle
Figure 3.7 shows a modern Siemens industrial gas turbine (SGT-750) with 37 MW nominal power
output.
D4.3 Energy system component units model library
16
2
Figure 3.7 – Siemens SGT-750 lightweight industrial gas turbine with 37 MW nominal ISO power output at a compressor
3
pressure ratio of 23.8:1 (picture from Siemens Energy ).
The ideal thermodynamic cycle (Joule/Brayton cycle) thermal efficiency (
) is as follows:
(3.21)
is the pressure ratio and
can be derived to [13]:
is the heat capacity ratio. The net specific work output (
)
(3.22)
Simplified definitions of thermal efficiency and specific net work output can also be derived for the
real cycle (compare, e.g., Lechner and Seume [13] or Razak [15]), including several parameters
such as combustor pressure loss and polytropic compressor and turbine efficiencies. However, the
simplified analytical and explicit descriptions do not take account of variations in material properties
due to changing temperature, pressure and species concentrations.
The maximum allowable turbine inlet temperature ( ) limits the maximum efficiency of gas
turbines. Temperature ( ) is accordingly limited. Hence, the thermal efficiency of the ideal cycle is
increased when the inlet air temperature ( ) is lower. Since gas turbines are constant (volumetric)
2
DLE burner: Dry-low emission burner based on lean premixed combustion.
Picture downloaded from www.siemens.com on 11/09/2015 at URL: http://www.energy.siemens.com/apps/features/sgt750_html/zoompieces/full_zoom.jpg.
3
D4.3 Energy system component units model library
17
flow engines (
), the power output of the gas turbine is increased, when the inlet air
temperature is lower. The net power output (
) can be derived as follows:
(3.23)
with the mass flow rate ( ), volumetric flow rate ( ) and density ( ). Since the ideal gas law is a
fairly good approximation for air [5], we can follow that:
(3.24)
Hence, the gas turbine net power output increases at lower inlet temperatures ( ) and higher
ambient pressures ( ). Thus, during day time where the ambient temperature is highest but also
the demand is highest, the available power output from the GT is reduced.
The power output and efficiency (depending on the design of the gas turbine) can be augmented
through the use of turbine inlet air cooling (TIAC). Al-Ibrahim and Varnham [16] and Ibrahim et al.
[17] categorized TIAC methods into:


Evaporative cooling: Small water droplets, fog or snow evaporate in the inlet air by drawing
energy from the inlet air. Hence, the inlet air is cooled. The capability of the compressor to
handle moist air must be checked.
Active cooling: Chilled water supplied to cooling coils by compression chillers, absorption
chillers or cold thermal energy storages extracts heat from the inlet air. Depending on the
initial humidity of the inlet air and the desired temperature, dehumidification may be required.
Economical and ecological performance of gas turbines can be improved through the use of TIAC
[18–21]. Through the use of thermal energy storages (e.g., ice storages), cooling loads can be
shifted to the night that have lower ambient temperatures and the performance of the gas turbine
system can be improved at peak times during the day [22–25].
Air can be described as moist air, a mixture of dry air and water (vapor, in most cases, when
unsaturated). The humidity ratio ( ) was defined as follows:
(3.25)
is the mass of water and
is the mass of dry air. Thus,
is not a mass fraction as the
previously used variables ( and ). The saturation partial pressure of water vapor ( ) was
described by Antoine [5] as function of the temperature ( in °C, in K):
(3.26)
D4.3 Energy system component units model library
18
Material properties of dry air and water were used for this equation and the following equations.
Table 3.1 summarizes the key parameters.
Table 3.1 – Material properties of dry air and water [5].
Parameter
Symbol
Value
Individual gas constants [J/kg/K]
Dry air
287.05
Water
461.52
Specific heat capacities [J/kg/K]
Dry air
1004.6
Water vapor
1863
Liquid water
4191
Ice
2070
Specific enthalpies of phase change [kJ/kg]
Vaporization
2500.9
Freezing
334
Triple point of water
Temperature [°C]
0.01
Pressure [kPa]
611.657
The humidity ratio ( ) and relative humidity ( )
r r lat d to on anoth r by Dalton’s la [5]:
(3.27)
(3.28)
With
, the humidity ratio at saturation ( ) is derived to:
(3.29)
In the following, quantities ( ) are specific values related only to dry air (e.g.
, different
to actual specific values related to the entity, e.g.
). The density of moist air could be
derived to [5]
(3.30)
(3.31)
Moist air can be unsaturated (with water vapor), just saturated, or supersaturated with water or ice
condensate. The specific enthalpy ( , related to the mass of dry air) for these states was derived
to [5]:
D4.3 Energy system component units model library
19
Unsaturated:
(3.32)
Saturated:
(3.33)
Supersaturated,
water condensate:
(3.34)
Supersaturated, ice
condensate:
(3.35)
Furthermore, three different temperatures could be defined for moist air:



Dry-bulb temperature ( and ): Common temperature, which is measured with thermometers
Dew-point temperature ( and ): Temperature to which moist air (at constant air pressure
and humidity ratio) is cooled to reach the state of saturation
Wet-bulb temperature ( and ): Lowest temperature, which evaporative cooling can reach.
The latter two temperatures could be computed based on the following two conditions:
(3.36)
(3.37)
These conditions must be satisfied to determine their respective temperatures.
h* [kJ/kg]
72 kJ/kg
81 kJ/kg
115 kJ/kg
unsaturated
43 kJ/kg
X e Evaporative
cooling
32.5 °C
1
25 °C
t
2e
23 °C
15 °C
2a
td
h
*
a
tw
supersaturated
Pole
0 °C
X a
(Water)
Active cooling
(and dehumidification)
(Ice)
10.8
18.9
21.7
32.3
X [g/kg]
Figure 3.8 – Evaporative (1  2e) and active cooling (1  2a) in a specific enthalpy ( in kJ per kg dry air) – humidity
ratio ( in g water per kg dry air) diagram. The required change of humidity ratio (
) for evaporative cooling and the
D4.3 Energy system component units model library
20
specific cooling energy (
) for active cooling as well as the change of humidity ratio due to dehumidification (
) are
indicated, as well as dry-bulb ( ), wet-bulb ( ), and dew-point temperature ( ). Areas of unsaturated, saturated and
supersaturated with water and ice condensate are marked.
The change of state due to evaporative and due to active cooling and dehumidification was plotted
in Figure 3.8. In addition to this, the dry-bulb, wet-bulb and dew-point temperatures were indicated
for State 1 (see green lines). Furthermore, the gas turbine ISO temperature (15 °C) was indicated.
State 2e can be reached by injecting water droplets that evaporate in the inlet air and hence cool
the inlet air. The temperature of State 2e strongly depends on the initial humidity (e.g.,
).
With a limited amount of required cooling energy, the inlet air could be cooled to dew-point
temperature. Through further cooling of the inlet air, even lower temperatures (State 2 a) could be
reached. However, to reach State 2a, the inlet air must be dehumidified and the required
condensation and removal of water vapour increases the amount of required cooling energy. The
given equations were sufficient to describe moist air in detail and evaluate evaporative and active
cooling options for TIAC.
3.4.5 Ice storages
A medium-scale ice storage with 250 kWh latent storage capacity was experimentally
investigated.4 Figure 3.9 shows the working principle of ice storages. Ice storages contain water in
an insulated tank with submerged heat exchanger tubes. When charging the ice storage, heat
transfer fluid with temperatures below 0 °C flows through these heat exchanger tubes. The
temperature of the water in the storage tank is reduced. Eventually, the water around the tubes
starts freezing to ice. When continuously extracting heat from the water and ice in the storage tank,
the ice layer around the tubes will grow. When the heat transfer fluid enters the storage with
temperatures greater than 0 °C, the ice storage is discharged. For the particular ice storage shown
in Figure 3.9 (an ice-on-coil internal-melt ice storage), the ice is melted from the inside. Hence, a
water layer builds up around the tubes and will grow with continuous discharge of the storage.
4
Originally th i
storag
od l as d v lop d ithin th EU Horizon 2020 proj t “SENSIBLE”. Th
implementation of this model into the energy system design method demonstration code was carried out
within the MODER project.
D4.3 Energy system component units model library
21
(a)
(b)
Charge 2
Q
3
Q
T
Heat transfer fluid
Charge
2
Ice
TPCM
Discharge 4
Q
1
3
1
4
Q
Water
Discharge
hPCM
h
Figure 3.9 – Ice thermal energy storage (ice-on-coil internal-melt):
(a) Principle of charging and discharging, (b) Ideal cycle [26].
The performance (or efficiency) of an ice storage could be described by the heat exchanger
effectiveness ( ). It was defined as follows [27]:
(3.38)
In Equation (3.38),
denotes the phase change temperature of water (0 °C). The heat
exchanger effectiveness can also be expressed in terms of the heat transfer coefficient ( ), heat
transfer area ( ) and the mass flow rate (
) and specific heat capacity (
) of the heat
transfer fluid:
(3.39)
The state of charge of the ice storage could be measured fairly easy. The water in the tank is never
completely frozen to ice. About 50% of the water remains liquid. Due to the different densities of
water (ca. 1000 kg/m³) and ice (ca. 920 kg/m³), the remaining water liquid level increases when
water freezes. Hence, the liquid level could be measured by a sensor. We denoted this state of
charge as volumetric state of charge.
For an experimental cooling system including compression chiller, cooling fans, cooling load and
ice storage, an empirical model was developed. The model would go beyond the scope of this
report. However, it was previously published in [9,10].
D4.3 Energy system component units model library
22
Figure 3.10 – Ice storage model validation.
The integral quantity volumetric state of charge is a fairly good indicator for the accuracy of the
overall cooling system model. Figure 3.10 shows that the model accurately predicted the
performance of the ice storage for a multitude of different data points included in this validation
data set.
3.5 Economic and regulatory boundary conditions
Parameters for the economic boundary conditions of energy conversion and energy storage units
were included in the model parameter tables in Appendix A. These parameters include in
particular:



Economical / Technical lifetime ( )
Specific invest ( )
Specific operation and maintenance costs (
)
Furthermore, start-up costs for energy conversion units were considered. These were modelled as
follows:
(3.40)
Numeric values for the parameter (
A.10.
) were also tabulated in the appendix in Table A.3 - Table
D4.3 Energy system component units model library
23
Regulatory boundary conditions strongly depend on the country and need to be investigated for the
individual case. Furthermore, the conditions were modified several times in the last few years (see,
e.g., [28]).
The model library with the energy system component unit models and the energy system design
method to be developed in WP4.4 shall be used for use case analysis.
D4.3 Energy system component units model library
24
4 Conclusion
In Task 4.3, an energy system component unit model library was developed.
First, candidates for energy conversion units and energy storage units were identified based on
typical energy demands in city districts. These components were then organized in an energy
system superstructure. A generic energy conversion and storage unit model was developed. Five
example models were introduced to show the way of how model parameters were identified.
Finally, the parameters for the model library were summarized in the appendix.
The target group of this study was the MODER consortium.
The model library is intended to be used further in WP4 in Task 4.4 for the energy system design
methods.
D4.3 Energy system component units model library
25
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D4.3 Energy system component units model library
29
Appendix
A. Model parameters5
For the tables shown below, the following abbreviations were used:





Experiment: The parameter was experimentally validated;
Physical model: A physical model was developed in MATLAB® and REFPROP and the
parameters were determined based on simulation;
Datasheet: Data derived from datasheets and/or personal communications with several
manufacturers.
Assumption: No references could be found, hence an assumption was made (probability >
90%);
Guess: No references could be found, the value was guessed (probability ca. 50%).
Table A.1 – Photovoltaic (PV) model parameters.
Variable Function of
,
,
Value / Model
1 kW – 10 MW
Source
[29–33]
1000 – 1800 €/kW
16 €/kW/a (12 – 40 €/kW/a)
25 a
Rated power capacity at 1000 W/m² global horizontal
irradiance; Temperature coefficient: 0.0045 1/K
[31,34,35]
[31,35]
[1]
Table A.2 – Wind turbine (WT) model parameters.
Variable Function of
,
-
Value / Model
100 kW – 8 MW
1200 – 1700 €/kW
30 €/kW/a (28 – 45 €/kW/a)
20 a
Fitted for 2 MW onshore wind turbine;
Cut-in wind speed: 2 m/s;
Rated wind speed: 11.94 m/s;
Furling wind speed: 25 m/s
Source
[31,34,36,37]
[31,34,35,38]
[35]
[2,4]
Table A.3 – Gas turbine (GT) model parameters.
Variable Function of
,
5
Value / Model
1 MW – 400 MW
Source
[34,36,39,40]
400 – 1300 €/kW
27 €/kW/a (16 – 36 €/kW/a)
25 a
medium
100 %/h
[31,34,39]
[31,39]
[41,42]
[13,43]
Prices are assumptions for energy system design and are not selling prices of Siemens AG.
D4.3 Energy system component units model library
30
Variable Function of
,
,
,
,
,
,
,
Value / Model
-100 %/h
Siemens SGT datasheet models
Physical model
Minimum exhaust temperature assumed to 100 °C (for
computing thermal efficiency)
Source
[13,43]
Physical
model;
[5,44–48]
Table A.4 – Steam cycle (ST) model parameters.
Variable Function of
,
-
Value / Model
1 MW – 400 MW
Source
[40]
500 – 1500 €/kW
27 €/kW/a (16 – 45 €/kW/a)
25 a
high
100 %/h
-100 %/h
0.38
1
Steam cycle without heat extraction
[34,39]
[31,34,39]
[41,42]
[43]
[43]
[49]
Assumption
[50,51]
Table A.5 – Internal combustion engine (ICE) CHP model parameters.
Variable Function of
,
,
,
Value / Model
1 kW – 20 MW
Source
[31,36,39,4
0,52]
700 €/kW – 4000 €/kW
27 €/kW/a (19 – 270 €/kW/a)
[31,39]
25 a
[31,39]
low
[41,42,53]
100 %/h
[54]
-100 %/h
[54]
0.5
[52]
Model based on published data (e.g., fits of performance [55]
curves provided by literature)
[52,55,56]
Table A.6 – Gas boiler (GB) model parameters.
Variable Function of
,
-
Value / Model
1 kW – 10 MW
50 - 600 €/kW
5.3 €/kW/a (3.7 – 6.7 €/kW/a)
20 a
low
100 %/h
-100 %/h
0.1
1
D4.3 Energy system component units model library
Source
Datasheet;
[31,36,40]
[31,36]
[31,57,58]
Guess
Assumption
Assumption
[59]
[59]
31
Variable Function of
Value / Model
0.974 (100% load); 0.97 (50% load)
Variable Function of
,
Value / Model
1 kW – 1 MW
Source
[60–62]
Table A.7 – Heat pump (HP) model parameters.
300 – 1000 €/kW
3.7 €/kW/a (rHP, 1.9 – 5.5 €/kW/a);
14 €/kW/a (HP, CHC, 5.5 – 22 €/kW/a)
15 a (rHP); 20 a (HP, CHC)
very low
100 %/h
-100 %/h
0.25 (decreasing with decreasing a b )
1 (decreasing with decreasing a b)
h
a b fit
Heat supply temperature: 50 °C (rHP); 80 °C (HP, CHC)
Reference COP (@ 40 °C lift): 2.5 (rHP); 4 (HP, CHC)
-
Source
Datasheet
[31,36]
[31,58]
Experiment
Experiment
Experiment
[63]
[63]
[31,63]
Table A.8 – Electric boiler (EB) model parameters.
Variable Function of
,
Value / Model
1 kW – 10 MW
-
60 – 300 €/kW
1.4 €/kW/a
15 a
none
100 %/h
-100 %/h
0
1
0.99
Source
Datasheet;
[36]
[36]
[58]
Assumption
Assumption
Assumption
Assumption
Assumption
[60]
Table A.9 – Absorption chiller (AC) model parameters.
Variable Function of
,
,
Value / Model
100 kW – 5 MW
AC0: 80 – 1000 €/kW; ACi: 600 – 1000 €/kW
2.3 €/kW/a
20 a
low
100 %/h
-100 %/h
0.2
1
Gordon-Ng absorption chiller model derived from
physical model
D4.3 Energy system component units model library
Source
Datasheet;
[40,64,65]
[40]
[58,66]
Guess
Assumption
Assumption
[67]
[67]
Physical
model;
32
Variable Function of
Value / Model
Source
[11,12,67–
69]
Table A.10 – Compression chiller (CC) model parameters.
Variable Function of
,
-
,
Value / Model
1 kW – 30 MW
80 – 500 €/kW
8 €/kW/a (CC)
15 a (rHP); 20 a (CC)
very low
100 %/h
-100 %/h
Model derived from datasheets
CCi, rHP: Reciprocating compressor (Bitzer 4PE12.F3Y, 134a)
CC0, CHC: Screw compressor (Bitzer CSVH38-290Y,
134a)
Cooling supply temperature: 12 °C (rHP); 8 °C (CC0,
CHC); -5 °C (CCi)
Condenser temperature difference: 10 °C (rHP); 3 °C
(CC0, CCi)
Source
Datasheet;
[40]
[40]
[58]
Experiment
Experiment
Experiment
[70,71]
Table A.11 – Lead-acid battery (LeadAcid) model parameters.
Variable Function of
,
Value / Model
1 kWh – 10 MWh
Source
[72]
-
120 – 180 €/kWh
0.46 €/kWh/a
10 a
8.34 %/h
-100 %/h
0.815
0.815
0.00708 %/h
[72]
[72]
[72–74]
[72–74]
[72]
[72]
[72]
Table A.12 – Lithium-ion battery (LiIon) model parameters.
Variable Function of
,
Value / Model
1 kWh – 10 MWh
Source
[72]
-
500 – 1000 €/kWh
0.44 €/kWh/a
15 a
100 %/h
-100 %/h
0.935
0.935
[72]
[72]
[72,75]
[72,75]
[72]
[72]
D4.3 Energy system component units model library
33
Variable Function of
-
Value / Model
0.00102 %/h
Source
[72]
Table A.13 – Hot water storage (HWS) model parameters.
Variable Function of
,
Value / Model
1 kWh – 100 MWh
-
6 – 80 €/kWh
0.1 €/kWh/a
40 a
20 %/h
-
-20 %/h
-
0.98
0.98
0.5 %/h
Source
Datasheet;
[40]
[72]
[31]
Experiment;
[76]
Experiment;
[76]
Experiment
Experiment
Experiment;
[77]
Table A.14 – Chilled water storage (CWS) model parameters.
Variable Function of
,
Value / Model
1 kWh – 100 MWh
-
30 – 200 €/kWh
0.1 €/kWh/a
40 a
15 %/h
-
-15 %/h
-
0.98
0.98
0.334 %/h
Source
Datasheet;
[40]
[72]
[31]
Assumption;
[76]
Assumption;
[76]
Assumption
Assumption
Assumption;
[77]
Table A.15 – Ice thermal energy storage (ITES) model parameters.
Variable Function of
,
Value / Model
1 kWh – 10 MWh
-
20 – 1000 €/kWh
0.1 €/kWh/a
25 a
20 %/h
-20 %/h
0.98
0.98
0.134 %/h
D4.3 Energy system component units model library
Source
Datasheet;
[40]
[72]
Experiment
Experiment
Experiment
Experiment
Experiment
Experiment
34