(493a) Modelling and Explicit Model Predictive Control for Combined Heat and Power System (CHP)
AIChE Annual Meeting
2013
2013 AIChE Annual Meeting
Computing and Systems Technology Division
Modeling and Control of Energy Systems I
Wednesday, November 6, 2013 - 12:30pm to 12:50pm
Modelling
and Explicit Model Predictive Control for Combined Heat and Power System (CHP)
N. Diangelakis, C.
Panos, E.N. Pistikopoulos
Centre for Process Systems Engineering,
Department of Chemical Engineering, Imperial College London, South Kensington Campus,
London SW7 2AZ, UK
Keywords:
Combined Heat and Power System, Mathematical modelling,
Explicit/Multi-Parametric Model Predictive Control, Parametric Programming
The concept of cogeneration, the
production of usable heat and power through a single process, is appealing
primarily for the low emission to total usable power ratio and secondarily for
the relatively low operational cost. Combined heat and power (CHP) systems
capture and use part of the by-product heat, released by an operating heat engine,
thus improving its overall efficiency. The environmental impact of the use of
CHP for covering electricity and heating demands is apparent when compared to
the use of multiple separate processes for the same purpose. The use of a power
generation unit's by-product heat results into using the same amount of fuel
and emitting the same amount of exhaust gases for the generation of both
electrical power and usable heat. This cost effective and environmentally
friendly process, compared to the use of separate units for electrical power
production and heating, is already an important part of emission reduction
policies ADDIN EN.CITE
<EndNote><Cite><Author>IEA</Author><Year>2009</Year><RecNum>25</RecNum><DisplayText>(IEA,
2009)</DisplayText><record><rec-number>25</rec-number><foreign-keys><key
app="EN"
db-id="zdzxrd0zlspvf7e92puvaaebxer9vt2eepdd">25</key></foreign-keys><ref-type
name="Personal Communication">26</ref-type><contributors><authors><author>IEA</author></authors></contributors><titles><title>Combined
Heat and Power: Cogeneration and District
Energy</title></titles><dates><year>2009</year></dates><pub-location>Paris</pub-location><publisher>OECD/IEA</publisher><label>CombinedHeatandPower:cogenerationanddistrictenergy</label><urls></urls></record></Cite></EndNote>(IEA,
2009). The great attention that CHP systems
have received as an alternative for integrated generation of heat and power is
attributed to their potential for a cleaner, more efficient power and heat
production strategy. The effective use
of CHP systems highly depends on factors such as the system components and
characteristics, the fuel type, the electrical and thermal loads that need to
be covered, the system's design and operating conditions. The necessity of CHP modelling
is therefore apparent not only in terms of the system's behavioural analysis but
also in order for the basis for both design optimization and optimal control to
be created.
In this work we focus on the
mathematical modelling, design optimization and control issues of CHP system
according to the framework ADDIN EN.CITE
<EndNote><Cite><Author>Pistikopoulos</Author><Year>2009</Year><RecNum>94</RecNum><DisplayText>(Pistikopoulos,
2009)</DisplayText><record><rec-number>94</rec-number><foreign-keys><key
app="EN"
db-id="zdzxrd0zlspvf7e92puvaaebxer9vt2eepdd">94</key></foreign-keys><ref-type
name="Journal
Article">17</ref-type><contributors><authors><author>Pistikopoulos,
E.
N.</author></authors></contributors><titles><title>Perspectives
in Multiparametric Programming and Explicit Model Predictive
Control</title><secondary-title>Aiche
Journal</secondary-title></titles><periodical><full-title>Aiche
Journal</full-title></periodical><pages>1918-1925</pages><volume>55</volume><number>8</number><dates><year>2009</year><pub-dates><date>Aug</date></pub-dates></dates><isbn>0001-1541</isbn><accession-num>WOS:000268413800001</accession-num><urls><related-urls><url><Go
to
ISI>://WOS:000268413800001</url></related-urls></urls><electronic-resource-num>10.1002/aic.11965</electronic-resource-num></record></Cite></EndNote>(Pistikopoulos,
2009), which compromises the followings
·
Development
of a high fidelity mathematical modelling - used for detailed simulation and
(design and operational) optimization studies.
·
Development
of a reduced order/approximating model, suitable for multi-parametric MPC
·
Design
of multi-parametric MPC controllers
·
Off-line
validation of the controllers
The
CHP's mathematical model consists of a detailed model for a natural gas
internal combustion engine (ICE) based on a mean value approach ADDIN EN.CITE
<EndNote><Cite><Author>Heywood</Author><Year>1989</Year><RecNum>23</RecNum><DisplayText>(Heywood,
1989)</DisplayText><record><rec-number>23</rec-number><foreign-keys><key
app="EN"
db-id="zdzxrd0zlspvf7e92puvaaebxer9vt2eepdd">23</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Heywood,
J. B.</author></authors><secondary-authors><author>Holman,
J.
P.</author></secondary-authors></contributors><titles><title>Internal
Combustion Engine
Fundamentals</title></titles><keywords><keyword>Internal,
combustion, engine, fundamentals</keyword></keywords><dates><year>1989</year><pub-dates><date>07</date></pub-dates></dates><publisher>McGraw-Hill,
Inc.</publisher><label>internalcombustionenginefundamentals</label><urls></urls></record></Cite></EndNote>(Heywood,
1989), ADDIN EN.CITE <EndNote><Cite><Author>Videla</Author><Year>2006</Year><RecNum>63</RecNum><DisplayText>(Videla
& Lie,
2006)</DisplayText><record><rec-number>63</rec-number><foreign-keys><key
app="EN"
db-id="zdzxrd0zlspvf7e92puvaaebxer9vt2eepdd">63</key></foreign-keys><ref-type
name="Generic">13</ref-type><contributors><authors><author>Videla,
J.</author><author>Lie,
B.</author></authors></contributors><titles><title>Simulation
of a small scale SI ICE based cogeneration system in
Modelica/Dymola</title></titles><keywords><keyword>simulation,
small chp, Internal combustion
engine</keyword></keywords><dates><year>2006</year></dates><label>SimulationofasmallscaleSIICEbasedcogenerationsysteminModelica/Dymola</label><urls></urls></record></Cite></EndNote>(Videla
& Lie, 2006), ADDIN EN.CITE
<EndNote><Cite><Author>Videla</Author><Year>2007</Year><RecNum>62</RecNum><DisplayText>(Videla
& Lie, 2007)</DisplayText><record><rec-number>62</rec-number><foreign-keys><key
app="EN" db-id="zdzxrd0zlspvf7e92puvaaebxer9vt2eepdd">62</key></foreign-keys><ref-type
name="Generic">13</ref-type><contributors><authors><author>Videla,
J.</author><author>Lie, B.</author></authors></contributors><titles><title>State/Parameter
Estimation of a Small-scale CHP
model</title></titles><keywords><keyword>state,
parameter, estimation, small chp,
model</keyword></keywords><dates><year>2007</year></dates><label>State/ParameterEstimationofaSmall-scaleCHPmodel</label><urls></urls></record></Cite></EndNote>(Videla
& Lie, 2007), ADDIN EN.CITE
<EndNote><Cite><Author>Konstantinidis</Author><Year>2010</Year><RecNum>29</RecNum><DisplayText>(Konstantinidis,
Verbatov, & Klemes, 2010)</DisplayText><record><rec-number>29</rec-number><foreign-keys><key
app="EN"
db-id="zdzxrd0zlspvf7e92puvaaebxer9vt2eepdd">29</key></foreign-keys><ref-type
name="Journal
Article">17</ref-type><contributors><authors><author>Konstantinidis,
D.</author><author>Verbatov, P.</author><author>Klemes,
J.</author></authors></contributors><titles><title>Multi-parametric
control and optimisation of a small scale
CHP</title><secondary-title>PRES 210: 13th International Conference
on Process Integration, Modelling and Optimization for Energy Saving and Pollution
Reduction</secondary-title></titles><pages>151-156</pages><volume>21</volume><dates><year>2010</year></dates><label>MultiparametriccontrolandoptimisationofasmallscaleCHP</label><urls></urls></record></Cite></EndNote>(Konstantinidis, Verbatov, & Klemes, 2010) and simplified dynamic models for the
throttle valve, the intake and exhaust manifolds, and the outer cooling system
(Figure 1). The ICE is modelled as a volumetric pump the working fluids of
which are the fuel ? atmospheric air mixture and the exhaust gases. The
volumetric efficiency is used to describe the engine's ability to aspire a
mixture of fluids and also to describe how the engine differs from an ideal
volumetric pump ADDIN EN.CITE ADDIN EN.CITE.DATA 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(Arsie,
Pianese, & Rizzo, 1998; Guzzella & Onder, 2010; Heywood,
1989;
Onovwiona, Ismet Ugursal, & Fung, 2007; Powell,
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. The ?evenly distributed process and effects? over an
engine working cycle, which a mean value model suggests, succeeds in capturing
the engine's behaviour in terms of power and heat production as a result of
combustion. In naturally aspired engines the break mean effective pressure,
reflects the ability to induct air, the effectiveness of air utilization in
combustion and the fuel conversion efficiency ADDIN EN.CITE
<EndNote><Cite><Author>Heywood</Author><Year>1989</Year><RecNum>23</RecNum><DisplayText>(Heywood,
1989)</DisplayText><record><rec-number>23</rec-number><foreign-keys><key
app="EN"
db-id="zdzxrd0zlspvf7e92puvaaebxer9vt2eepdd">23</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Heywood,
J.
B.</author></authors><secondary-authors><author>Holman,
J.
P.</author></secondary-authors></contributors><titles><title>Internal
Combustion Engine Fundamentals</title></titles><keywords><keyword>Internal,
combustion, engine, fundamentals</keyword></keywords><dates><year>1989</year><pub-dates><date>07</date></pub-dates></dates><publisher>McGraw-Hill,
Inc.</publisher><label>internalcombustionenginefundamentals</label><urls></urls></record></Cite></EndNote>(Heywood,
1989). The break mean effective pressure is
determined by taking into consideration the thermodynamic efficiency of the
engine, the fuel mean effective pressure, the total external losses in terms of
pressure and the upstream and downstream pressure difference of the ICE's
working fluids. The engine block's surface area in contact with the coolant the
engine block's area in contact with the ambient environment and the cylinder
wall's surface area in contact with the coolant are derived using assumptions
regarding the shape of the engine block, the spatial placement of the cylinders
and the cooling channels that run through the engine block. The heat transfer
among the different engine parts makes the engine's spatial characteristics a
significant operating factor.
Figure SEQ Figure \* ARABIC 1 Graphical Representation of the CHP
Model
The
throttle valve is used to manipulate the amount of atmospheric air that enters
the ICE. The compressible flow of atmospheric air that flows through the valve
is assumed to change between laminar and turbulent according to the throttle
vale open area ADDIN
EN.CITE
<EndNote><Cite><Author>Moran</Author><Year>1992</Year><RecNum>37</RecNum><DisplayText>(Moran
& Shapiro,
1992)</DisplayText><record><rec-number>37</rec-number><foreign-keys><key
app="EN"
db-id="zdzxrd0zlspvf7e92puvaaebxer9vt2eepdd">37</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Moran,
M.</author><author>Shapiro, H.
N.</author></authors></contributors><titles><title>Fundamentals
of Engineering
Thermodynamics</title></titles><dates><year>1992</year></dates><pub-location>New
York</pub-location><publisher>Wiley</publisher><label>FundamentalsofEngineeringThermodynamics</label><urls></urls></record></Cite></EndNote>(Moran
& Shapiro, 1992). Due to the widely spread use of direct injection
engines the fuel is assumed to be sprayed directly into the engine cylinders,
thus minimizing any fuel losses and maximizing the engines efficiency ADDIN EN.CITE
<EndNote><Cite><Author>Heywood</Author><Year>1989</Year><RecNum>23</RecNum><DisplayText>(Heywood,
1989)</DisplayText><record><rec-number>23</rec-number><foreign-keys><key
app="EN"
db-id="zdzxrd0zlspvf7e92puvaaebxer9vt2eepdd">23</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Heywood,
J.
B.</author></authors><secondary-authors><author>Holman,
J.
P.</author></secondary-authors></contributors><titles><title>Internal
Combustion Engine Fundamentals</title></titles><keywords><keyword>Internal,
combustion, engine, fundamentals</keyword></keywords><dates><year>1989</year><pub-dates><date>07</date></pub-dates></dates><publisher>McGraw-Hill,
Inc.</publisher><label>internalcombustionenginefundamentals</label><urls></urls></record></Cite></EndNote>(Heywood,
1989). The intake and exhaust manifolds are
modelled as small tanks, prior to and after the cylinder ports that manipulate
the intake air pressure and exhaust gas outlet pressure, respectively. Through
the outer cooling system, the heat produced by the ICE can be usable, thus
turning a simple reciprocating internal combustion engine into a highly
efficient cogeneration system. The two sources of heat are the recirculating
engine coolant and the hot exhaust gases, which form the stage one and stage
two interactions with the outer cooling system, respectively.
The
dynamic mathematical model of the system implemented in gPROMS® (PSE, Ltd.) and
the simulation results show that the mathematical model can accurately predict
the behaviour of the actual system. The objective of the design optimization is
to estimate the minimum displacement volume of the internal combustion engine
while satisfying the maximum electrical demand of a residential 10-house district.
The optimization takes place in gPROMS® (PSE, Ltd.) with the implementation of
a control vector parameterization algorithm via single-shooting; and manages to
estimate the minimum internal combustion engine displacement volume under
electrical power production constrains.
Finally, two controllers where designed, the
first of which manipulates the inlet flow-rate of atmospheric air and fuel into
the engine for specific electrical power production set points, while the
second manipulates the cooling water flow-rate for hot water production of a certain
temperature range. The design and testing of the controller is implemented in gPROMS®
(PSE, Ltd.) and MATLAB® (MathWorks, Inc.) with the use of gOMATLAB® (PSE, Ltd.)
and POP(Parametric Optimization Programming (ParOS) Ltd.). The designed explicit/multi-parametric
model predictive control (MPC) manages to control the power production system and
water heating system while satisfying the constraints of the process.
References
ADDIN EN.REFLIST Arsie, L., Pianese, C., & Rizzo, G. (1998).
Models for the Prediction of Performance and Emissions in a Spark Ignition
Engine. SAE paper 980779.
Heywood,
J. B. (1989). Internal Combustion Engine
Fundamentals: McGraw-Hill, Inc.
IEA
(2009). [Combined Heat and Power: Cogeneration and District Energy].
Moran,
M., & Shapiro, H. N. (1992). Fundamentals
of Engineering Thermodynamics. New York: Wiley.
Videla, J., & Lie, B. (2007). State/Parameter Estimation of a
Small-scale CHP model.