Modelling and Explicit Model Predictive Control for Combined Heat and Power System (CHP)

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>&lt;Go to ISI&gt;://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 &amp; 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 &amp; 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, &amp; 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 &amp; 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.

Guzzella, L., & Onder, C. H. (2010). Introduction to Modeling and Control of Internal Combustion Engine Systems (2nd ed.): Springer.

Heywood, J. B. (1989). Internal Combustion Engine Fundamentals: McGraw-Hill, Inc.

IEA (2009). [Combined Heat and Power: Cogeneration and District Energy].

Konstantinidis, D., Verbatov, P., & Klemes, J. (2010). Multi-parametric control and optimisation of a small scale CHP. PRES 210: 13th International Conference on Process Integration, Modelling and Optimization for Energy Saving and Pollution Reduction, 21, 151-156.

Moran, M., & Shapiro, H. N. (1992). Fundamentals of Engineering Thermodynamics. New York: Wiley.

Onovwiona, H. I., Ismet Ugursal, V., & Fung, A. S. (2007). Modeling of internal combustion engine based cogeneration systems for residential applications. Applied Thermal Engineering, 27(5--6), 848-861.

Pistikopoulos, E. N. (2009). Perspectives in Multiparametric Programming and Explicit Model Predictive Control. Aiche Journal, 55(8), 1918-1925. doi: 10.1002/aic.11965

Powell, J. D. (1987). A Review of IC Engine Models for Control System Design. Paper presented at the Proceedings of the 10th IFAC World Congress, San Francisco, CA.

Videla, J., & Lie, B. (2006). Simulation of a small scale SI ICE based cogeneration system in Modelica/Dymola.

Videla, J., & Lie, B. (2007). State/Parameter Estimation of a Small-scale CHP model.