#
A Comprehensive Review and Qualitative Analysis of Micro-Combined Heat and Power Modeling Approaches^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Review of the Models

#### 2.1. Annex 42 Models

_{net}, and the temperature of the cooling water to the cooling water control volume, T

_{cw}

_{,i}. The model then uses a correlation for fuel-to-electric conversion efficiency, η

_{e}, to calculate the fuel consumption of the engine, Q

_{gross}, as in Equation (1):

_{e}, is a function of the flow rate of the cooling water, m

_{cw}, the temperature of the cooling water at the inlet to the cooling water control volume, T

_{cw}

_{,i}, and the electric demand. The authors suggested a tri-variate second-order polynomial form as in Equation (2):

_{q}, is defined as the ratio of recoverable heat to the fuel consumption of the engine. The authors suggested a form similar to η

_{e}as shown in Equation (3):

_{gen}, is then calculated as in Equation (4):

_{loss}, and is assumed to be proportional to the difference between the bulk average engine temperature, T

_{e}, and the temperature of the surrounding ambient, T

_{a}, as in Equation (5):

_{loss}is the overall effective thermal conductance between the engine control volume and the surroundings. Another portion of the recoverable heat is recovered into the cooling water stream, Q

_{HX}. This portion is calculated based on an overall thermal conductance between the cooling water and the engine, [UA]

_{HX}, as in Equation (6):

_{cw}

_{,o}is the temperature of the cooling water at the outlet of the cooling water control volume. An energy balance is then performed on the engine control volume as in Equation (7) and the cooling water control volume as in Equation (8):

_{e}is the bulk thermal capacitance of the engine block and its internal heat exchangers. [MC]

_{cw}is the overall thermal capacitance of the encapsulated cooling water in the system and the heat exchangers in immediate contact with the encapsulated cooling water. C

_{cw}is the specific heat of the cooling water. T

_{cw}

_{,i}is the temperature of the cooling water at the inlet to the cooling water control volume.

_{e}, the b coefficients of η

_{q}, [UA]

_{loss}, [UA]

_{HX}, [MC]

_{e}and [MC]

_{cw}. These parameters however are not easy to calculate and in most, or all, cases these parameters will have to be estimated empirically.

_{e}/12.5 kW

_{t}ICE cogeneration device and later validated the model. The calibration and validation used datasets from an installation that did not follow the experimental protocol but nevertheless provided rich data for calibration and validation. The coefficients of both η

_{e}and η

_{q}were determined from steady state measurements at different levels of electric power demand, cooling water flow rates and cooling water inlet temperature. The influence of cooling water temperature and cooling water flow rate on η

_{e}and η

_{q}was considered to be insignificant. The thermal capacitances ([MC] values) and the thermal conductance ([UA] values) were estimated using parameter identification process. The boundary and initial conditions were fed to the model and the outputs were compared to the actual data. The [MC] and [UA] values were varied to minimize the error between the model output and the actual data. This study used a generic platform independent optimization program, GenOpt to determine the [MC] and [UA] values. GenOpt enables automatic optimization using advanced search techniques to determine optimal design parameters by minimizing the cost function. GenOpt drove the simulation software incorporating the customized cogeneration device model over multiple simulations. The power output required from the generator, the coolant inlet mass flow rate and coolant temperature were derived from experimental data and used as inputs to the simulation model. The target optimization parameter was the cooling water outlet temperature, as it was the principal coupling variable between the cogeneration model and the integrated system model. The calibration parameters are summarized in Table 1.

_{e}/11.5 kW

_{t}natural gas fueled 952 cm

^{3}reciprocating ICE µCHP [15] capable of modulating its output. The thermal recovery from the water-glycol coolant mixture was accomplished in a plate heat exchanger and stored in a water tank. The stored heat was directly utilized for building heating during the winter while indirectly utilized for cooling via a lithium chloride absorption heat pump during the warm season, as shown in Figure 2 below. Rosato et al. conducted a thorough experimental campaign under a range of controlled boundary conditions to generate a data set encompassing both steady-state and transient operational scenarios. Hundred and three empirically derived coefficients were acquired from the calibration tests and used as inputs to the model, specific to the prime mover investigated. The key approach included measuring primary energy consumption, electric power production and thermal output to generate calibration data for the model. Detailed calibration procedures to determine the 103 model parameters were described.

_{e}residential building integrated micro-cogeneration system operated during the heating season using the TRNSYS dynamic platform [17]. This study comprised of a CHP system supported by heat exchangers and auxiliary boilers. Parametric analysis of the system was conducted in a similar fashion as that utilized by Rosato et al. [15]. Additionally, the model was integrated with hot water storage tank model, boiler model, and subjected to analysis in different building types and climatic zones while supporting electric, space heating and water heating loads. Primary energy savings were analyzed as a function of electric and thermal load following scenarios and concluded that a larger thermal energy storage tank was necessary to optimize the efficiency under any operating mode.

#### 2.2. Independent Models

_{e}Otto cycle engine [19]. The research team developed and tuned the model to match steady state test results followed by validation with transient experiment results. The effect of regional variation, and the impact of thermal energy storage were also investigated. The test unit consisted of several heat exchangers connected in series and finally integrated with hot water storage tank via a plate heat exchanger. The engine was modeled using type 907 component in TRNSYS using empirical performance data to determine the operating outputs. The desired electric output derived the efficiency, and exhaust quality using the performance map. Schematic of the laboratory µCHP system configuration utilized in this study are shown in Figure 3 below. In addition to the PM, this work modeled the storage tank as a fluid filled constant volume tank divided into isothermal temperature nodes to simulate the stratification environment. Thermal loss from the tank to ambient was determined through empirical data at fully heated state. Experimental results were used for the steady state calibration by operating the PM at fixed speed while discarding the heat to the outdoors. Validation experiments revealed a 1.7% deviation in the observed thermal output and considered satisfactory, given the measurement uncertainty and approximations for exhaust gas specific heat values.

_{e}µCHP device considering overheat protection controls. This group focused on addressing the mismatch between energy demand and supply while optimizing the system design and operation/control strategy [21]. The authors developed a new model in TRNSYS software platform environment by implementing overheat protection control and status parameters of the exhaust gas. Overheat protection controls the temperature of the engine (primary circulation fluid) and cooling water (secondary circulation fluid) below the set point values. The unique aspect of this µCHP system was its ability to operate in manual, thermal priority, and electrical priority modes. A schematic of the experimental setup is shown in Figure 4 below.

_{overheat}is heat transfer from the engine control volume to the surroundings through the cooling radiator, while ε

_{pro}is the on(1)/off(0) state of the overheat protection control:

_{out}) vs. power required (P

_{req}) under transient conditions. The delay time τ accounts for the step input response of a first-order linear time-invariant system, set at ~63% of the final value. This approximation simplified the model for a very low computational time. The authors presented a detailed analysis of transient response of each component in a separate work [25]. The correlations between exhaust gas temperature, electric efficiency, and electric power output were adopted from previous work [26]. The architecture of the complete simulation model utilized in this work is shown in Figure 6. One of the key differentiating factors of this model was integration of the thermal energy storage (TES) module represented by Equation (13) and electric energy storage (EES) module represented by Equation (14):

_{e}is the thermal efficiency:

_{ign}is the ignition angle, ϑ

_{d}is combustion duration time, ϑ is the crankshaft angle, α was assumed to be 5 and n = 3. Instantaneous characteristic gas velocity was represented by the term U

_{p}(ϑ), P is the pressure, b is the cylinder bore diameter, m is the mass flow rate, and R is the gas constant:

_{g}is thermal conductivity coefficient, B is piston bore, Re is the Reynolds number, b is Annand constant, T

_{g}is the zonal temperature, and T

_{w}is the wall temperature. Twenty one ODEs representing the complete ICE system’s thermodynamic model were solved in MATLAB using the non-stiff ODE solvers ode113 and ode45. This model was later successfully validated using specification sheets for natural gas fueled CHP-ICE modules. The optimal integrated ICE-ORC CHP system was later shown to achieve up to 30% higher power output than a nominal ICE based configuration. This study also looked at different CHP capacities and concluded that the heat recovery factor was more favorable in medium-sized engines. This study provided a very broad overview of the modeling approach and its impact on system performance. It also provides very useful insights in to modeling considerations and their impact on hybrid systems involving waste heat recovery utilization.

_{th}

_{,boil}is the thermal power provided by the boiler, P

_{th}

_{,CHP}is the thermal power provided by the CHP, P

_{th}

_{,us}is the thermal power required by the user, U and S are thermal transmittance and surface area of the tank while T is the temperature.

_{j}(0) is the initial value of the energy contained in the storage unit, and Φ

_{j}

_{,in}, Φ

_{j}

_{,out}, and Φ

_{j}

_{,L}are the total amount of energy sent to, taken from and lost by the storage unit in the time period 0 to τ, respectively. The author then demonstrated the application of the proposed guidelines of the generic model to develop an optimum design and operation of a set of devices serving the thermal and electrical loads of the user via a hybrid PV configuration in a district heating network. Additionally, system design optimization and energy storage optimization was also presented in detail by considering linear characteristic maps of the energy conversion units and applying linearization technique to the nonlinear constraints.

_{el}micro-cogeneration plant was modeled by utilizing all waste heat streams in the gasification processes ranging from feed drying to syngas generation. The interactions between different unit operations were modeled, optimized, and validated. A comprehensive thermodynamic model was developed using Thermoflex

^{TM}(Thermoflow Inc., Florida, USA) and GT-Suite

^{®}(Gamma Technologies, LLC, Illinois, USA) software tools for modeling the gasifier and the engine respectively. GT-Suite

^{®}is a one-dimensional simulation tool for evaluating concepts and detailed systems analysis and optimization of diverse chemical and mechanical systems. The optimization process was done using modeFRONTIER

^{®}(ESTECO SpA, Trieste, Italy) software package. The authors presented favorable operating conditions for a balanced system operation with further recommendations for optimal design configuration. Similarly, Chang et al. utilized the Thermoflex

^{TM}and GT-Power platforms (Gamma Technologies, LLC, Illinois, USA) to model a rice husk-based biomass fueled ICE CHP system. The authors showed the influence of gas composition on overall efficiency by modifying the 1D numerical model representing the engine.

_{el}system. The authors however did not discuss their model calibration and validation methods.

_{e}Otto cycle engine for meeting the energy needs of a residential building was studied by Jung et al. [43]. The authors utilized TRNSYS software package for developing the simulation model to operate the CHP in thermal load following mode. The CHP model was combined with a stratified tank via a plate heat exchanger after recovering the heat from engine cooling jacket, oil coolant, exhaust gas and the generator, similar to the configuration shown in Figure 7. Calibration of the TRNSYS ICE module was carried out using experimental data from both steady state and transient state measurements. The error in fuel use and electrical output was negligible and the thermal output error was reported as 1.7%. Standalone stratified tank calibration and validation was carried out with experimental results. This study also observed a peak error of 4.8% without tank model and 7.4% with tank model, between experimental and simulation predictions.

_{v}is the specific heat of water, V is the volume of thermal mass, ρ is the density of water, T

_{TM}is the thermal mass temperature, Q

_{pelt}is the rate of heat rejection through the Peltier. Q

_{in}is the heat flux from the copper pipe (Equation (23)) and Q

_{amb}is the thermal loss to environment (Equation (24)), h is the convection heat transfer coefficient, m

_{TM}is the mass flow rate of the hot water through copper pipe, As is the convection surface area, T

_{in}and T

_{out}are the temperature of the water at the inlet and outlet of the copper pipe, the subscript t indicates the tank thermal mass, while subscript C refers to the copper pipe:

_{e}ICE-based system was studied [45]. This study developed a model, based on thermodynamic equilibrium calculations in Engineering Equation Solver (EES), was later validated using values from the open literature. Exhaust gas stream from the ICE was utilized in treating the biomass feed for optimizing the size and overall system efficiency.

_{c}) according Equation (29), and radiative heat transfer coefficient (h

_{r}) according to Equation (30):

_{w}, ω represent area of heat transfer, cylinder wall temperature, and average speed of gas at cylinder, respectively. Also, k

_{gas}, ρ

_{gas}, B and µ

_{gas}are piston speed, gas thermal conductivity, cylinder bore and gas dynamic viscosity, respectively. Together, these governing equations predicted the rate of heat output in various components of the IC engine. Stirling engine modeling was conducted using a set of differential equations. The key differentiating factor in this modeling approach was the simplicity and calculation speed without needing combustion details. The zero-dimensional models are divided into different zones, similar to the control volume approach used in majority of the previous models but using double-Wiebe function to predict the unburnt fuel mass. The authors also laid out a flow chart of the CHP modeling approach where the first step involves technical specifications of the engine along with initial conditions of the IC for the zero-dimensional model. The next step involves utilizing the evaluated temperature and heat output of exhaust gases for the heater of the stirling engine. A combined analysis of both engines predicted complete technical, economic, and environmental value of the CHP.

_{Cali}and Output

_{Mesi}are respectively the i

^{th}calculated and measured output values and n is the total number of measured output data. The ANN-based model was shown to provide reliable engine performance parameters of electrical and thermal outputs however the integration of the engine with a true micro-CHP model including the intermediate heat exchanger for thermal utilization was not carried out.

_{e}ICE—Geothermal heat pump system optimized for specific building applications via multi-criteria method based on energy, economic and environmental factors [50]. Conservation laws were applied for energy balancing while a simple correlation relating efficiency (η

_{EL}) to electric power (E

_{ICE}), shown in Equation (32). The waste heat output of the exhaust gas (Q

_{ex}) and coolant (Q

_{jw}) were determined via polynomial fitting curves, shown in Equations (33) and (34), where b and c constants and PLR

_{ICE}is the part load ratio:

_{e}to 9 MW

_{e}, and notied that the electrical efficiency drops by ~5% while thermal efficiency increases by 5% when an engine is operated at 50% of the rated power. This study proposed two simple two-layer feed-forward neural network fits to predict the average performance between 50% to 100% part-load levels. The networks were trained using Levenberg-Marquardt back propagation algorithm and 10 hidden neurons. 70% of the data points were used for training, and 15% each for validation and testing. The authors also presented heat exchanger (HEX) modeling methodology where these HEXs were discretized into series of equal temperature or equal enthalpy increments.

## 3. Discussion and Conclusions

- Develop/refine models to address discrepancies associated with transient behavior—startup, cool-down, stand-by, interval between start and stop cycles, and delay time in these transient conditions. These aspects have been shown to improve the thermal efficiency of the system and are crucial for a reliable model.
- Develop reliable schemes to analyze the performance of thermal and electric energy storage modules over a broad range of operating conditions. These models must be designed such that the integration-related discrepancies are accounted for appropriately.
- Properly account for condensation of the flue gas exhaust stream in the PM model as well as its integration with thermal storage model
- Simulation results have been proven to be impacted significantly by the time-step used in the model. This factor must be considered for developing the model and utilizing the calibration data in a meaningful form
- Broader operational and experimental results need to be collected to study and characterize the PM thoroughly
- Storage system model must balance the accuracy of the PM model
- System design approaches focusing on cold climate applications—µCHP systems are ideal resources for cold climate applications where the heat demand is high, and the grid resources are vulnerable
- Thorough consideration of the governing physics and chemistry of the model to improve the accuracy of complex systems
- Expansion of the µCHP model to integrate thermally driven heat pump technology for maximizing the energy efficiency
- Examination of co/trigeneration system models for applications in communities, non-residential buildings, and other large facilities
- Application of these models to address commercialization issues to help wider market adoption.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

CHP | Combined Heat and Power |

DG | Distributed Generation |

EES | Electric Energy Storage |

GHG | Green House Gas |

HX | Heat Exchanger |

ICE | Internal Combustion Engine |

IEA | International Energy Agency |

kW | Kilo Watts |

µCHP | Micro CHP |

MW | Mega Watts |

NG | Natural Gas |

ORC | Organic Rankine Cycle |

PEMFC | Proton Exchange Membrane Fuel Cell |

PHX | Plate Heat Exchanger |

PM | Primary Mover |

RPM | Revolutions Per Minute |

SOFC | Solid Oxide Fuel Cell |

TES | Thermal Energy Storage |

TRNSYS | Transient System Simulation Tool |

HEX | Heat Exchanger |

Symbols | |

a: b | Coefficients |

A | Area |

C | Thermal conductance |

cp | Specific heat at constant pressure |

$\partial $ | Partial derivative |

E | Energy |

H | Enthalpy |

L | Length |

MC | Bulk thermal capacitance |

m | Mass |

η | Efficiency |

P | Power |

Q | Heat energy |

r | Radius |

Re | Reynolds number |

t | time |

T | Temperature |

τ | Time Delay Constant |

U | Heat transfer coefficient |

x | Concentration |

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**Figure 1.**Generic engine model control volumes, Annex 42 modeling strategy (IEA ECBCS Program). Mass transfer in purple and heat transfer in blue.

**Figure 3.**CHP system configuration used in the TRNSYS modeling of an NG fueled Otto engine. Integration of the PM in a µCHP configuration.

**Figure 4.**Experimental setup of a 25 kW

_{e}µCHP system adopted by Zheng et al. for developing a new model in the TRNSYS platform.

**Figure 5.**µCHP modeling approach with four different control volumes to address overheat protection.

**Figure 6.**Simulation architecture used in transient operation model developed by Ippolito F., and Venturini M. DHG-District heating grid, EG-Electric grid, EES-Electric energy storage, TES-Thermal energy storage, PM-Primary mover. Green line represents electric power flow, Orange line represents thermal power flow. Blue lines represent corresponding electrical thermal requirements from the user.

η_{e} | 0.27 | η_{q} | 0.66 |

[UA]_{loss} | 13.7 W/K | [UA]_{HX} | 741 W/K |

[MC]_{e} | 63,605.6 J/K | [MC]_{cw} | 1000.7 J/K |

Temperature, T | Interval k | QO(ieg) | QO(iac) | QO(ijw) | QO(ilo) | QD(jas) | QD(jad) |
---|---|---|---|---|---|---|---|

X deg C | 1 | ||||||

Y deg C | 2 | ||||||

. | . | ||||||

. | . | ||||||

. | . | ||||||

. | . | ||||||

25 deg C | k |

Prime Mover, (kW) | Energy Storage | Approach/Methodology | Advantages | Optimization | Ref |
---|---|---|---|---|---|

Combustion Engines, Fuel Cells (<15 kW_{e}) | Hot water storage tank | Control Volume. Model calibration with empirical data | Simplicity, reliability if empirical data is utilized | Thermal capacitance and conductance optimization with GenOpt | [13] |

ICE, 5.5 kW_{e} | Simulation in TRNSYS, ESP-r, Energyplus | Annex 42 model-based control volume approach | Non-traditional calibration procedure—using optimization tools | single- and multi-objective optimization algorithms | [14] |

ICE, 6 kW_{e} | Hot water tank | Annex 42 modelling approach. Electric load following mode | Detailed calibration methodology, Transient mode considerations | GenOpt optimization approach | [15,16] |

ICE, 6 kW_{e} | Variable capacitance hot water storage tank | TRNSYS dynamic platform, control volume approach | Parametric study similar to 14; Sensitivity of energy flow with variable thermal storage volume | Electrical and thermal load following modes of operation to optimize the savings | [17] |

Otto cycle Engine, 4 kW_{e} | Hot water storage tank, stratified model | TRNSYS component-based model. | Detailed transient test approaches and their implications on model reliability | Model tuned to match simulated outputs with experimental results | [19] |

ICE, 25 kW_{e}, CCHP | TRNSYS hot water storage tank module-based model | Modified Annex 42 approach with additional control volume preventing overheating via bypass loop | Models ability to operate in manual, thermal priority and electrical priority modes. High level of model detail and calibration methodology | Dynamic simulation model without the need for any optimization | [21] |

Reciprocating Gas Engine, 1.3 MW_{e} | Thermal storage tanks | Dynamic and steady-state performance data from an operating plant was used to develop the model using engineering principles | Reliable dynamic performance prediction | - | [22] |

ICE, <50 kW_{e} | Thermal and Electrical Storage | Six different components (including user demand) in the CHP were independently modeled | Implementation of delay subsystem yields high transient performance reliability. | Optimal thermal and electrical energy storage-based configurations. Simplified representation of dynamic effects | [24,25] |

Otto Engine, 125 kW_{e} | Stratified thermal storage module | Three different levels of stratification were modeled along with all energy flows | Influence of temperature level in the tank on energy efficiency and economics is modeled | - | [28] |

ICE-ORC Hybrid, 2.5–5 MW | None | ODEs representing conservation laws while using reliable heat transfer correlations such as Wiebe, Woschini, and Annand | Provides guidelines on suitable ICE designsfor waste heat recovery projects | Whole system optimization framework. | [33] |

Generic CHP Model | Flexible design consideration | Based on Mixed-Integer Non LinearProgramming (MINLP) | Generic dynamic modeling approach. Provides guidelines for system definition, and specification. | Generic, low computational effort framework | [38] |

ICE, 15 kW_{e} | Waste heat recovery and direct utilization | Modeled according to the continuity, momentum, and energy equations through 1D thermo-fluid dynamic characterization | Flexible waste heat recovery system with multiple temperature levels of thermal output | Optimal sizing of the polygeneration plant based on flexible heat recovery | [41] |

Otto Engine, 4 kW_{e} | Stratified storage tank model | TRNSYS component based model, calibrated with empirical data | Application of commercial software to design, optimize and validate a complete residential building CHP system | TRNSYS optimization | [43] |

Hybrid ICE-Stirling, 85 kW_{e} | Direct heat utilization | Zero-dimensional mathematical model with single zone consisting of operating fluid as the thermodynamic system | Simplified system representation with high reliability | Electrical output optimization via waste heat utilization in secondary power generation unit | [46] |

Biogas-Diesel ICE, 3.5 kW_{e} | No thermal storage | Artificial Neural Network (ANN) based approach while minimizing the RMSE value | Reliable engine performance prediction showing the electrical and thermal outputs | Iterative selection data optimization for ANN design optimization. | [47] |

3MWe, polygeneration system | None | Open Problem Table (OPT) combining pinch analysis with MILP | Novel approach for complex systems containing multiple sources and sinks | MILP model with multiple decision variables | [48] |

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**MDPI and ACS Style**

Cheekatamarla, P.; Abu-Heiba, A.
A Comprehensive Review and Qualitative Analysis of Micro-Combined Heat and Power Modeling Approaches. *Energies* **2020**, *13*, 3581.
https://doi.org/10.3390/en13143581

**AMA Style**

Cheekatamarla P, Abu-Heiba A.
A Comprehensive Review and Qualitative Analysis of Micro-Combined Heat and Power Modeling Approaches. *Energies*. 2020; 13(14):3581.
https://doi.org/10.3390/en13143581

**Chicago/Turabian Style**

Cheekatamarla, Praveen, and Ahmad Abu-Heiba.
2020. "A Comprehensive Review and Qualitative Analysis of Micro-Combined Heat and Power Modeling Approaches" *Energies* 13, no. 14: 3581.
https://doi.org/10.3390/en13143581