# Modeling On-Site Combined Heat and Power Systems Coupled to Main Process Operation

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## Abstract

**:**

## 1. Introduction

- At the plant level, decisions are related to the quantity of electricity that must be bought from the external grid, or generated on site in order to sell a surplus if possible. Here, different contracts (Base load, Tarif of Use (TOU)), and electricity markets (Day-ahead market, intra-day market) are usually considered, and the price of the electricity takes on a special relevance.
- At the equipment level, once the quantity of electricity to be generated has been decided, the next step is to decide what equipment is going to be used; this is known as the Unit-Commitment (UC) problem. Then, the load generation of each of the selected pieces of equipment is decided. This is the Economic Dispatch (ED) problem.

## 2. Case Study

## 3. Obtaining the Model

- Beet production rate (${W}_{BStOut}$) [370–430 T/h].
- Electricity power generation (${E}_{Tu}$) [5000–11,000 kW].
- Evaporation working pressure (${P}_{SSaOut}$) [2.2–3.0 barA].
- Superheated steam temperature obtained in boilers (${T}_{SBo}$) [360– 420 ${}^{\circ}\mathrm{C}$].

- Electricity consumption of the sugar factory (${E}_{p}$).
- Natural gas mass flow needed to operate the whole process (${W}_{G}$).
- Average time beet spends in the storage zone (${\tau}_{St}$).
- Steam pressure inside the fourth effect of the evaporation (${P}_{IV}$).
- European legislation Indexes.
- Heat energy consumption of the sugar factory (${Q}_{p}$).

#### 3.1. Main Process

#### 3.2. Heat Consumption

^{®}system identification toolbox [37] is used, and the model obtained is shown in Equation (2). The validity of this model is shown in the next section along with the rest of the model.

#### 3.3. Electricity Power Consumption

#### 3.4. Pressure Inside Fourth Effect

#### 3.5. Storage Zone

#### 3.6. Boilers

#### 3.7. Expansion Zone

#### 3.8. Saturator

#### 3.9. Relief Valve

#### 3.10. European Legislation

## 4. Validation

^{®}[41], an object oriented modeling and simulation software. Several experiments, which are shown in Figure 10, have been carried out to test the response of the model. These tests correspond to different typical operational points.

#### Discussion of the Results

## 5. Extension to Other Case Studies

- Establishment of the simulation objectives.
- Set model inputs and outputs.
- Search for relations between the inputs and outputs.
- 3.1.
- Look for control volumes to disaggregate the model.
- 3.2.
- Select where to apply first principles or experimental models.

- Experimental modeling.
- 4.1.
- Analyze the response of the selected outputs, when steps are performed in the inputs.
- 4.2.
- Check linearity between the inputs and outputs selected.
- 4.3.

- Parametrization of the model.
- Symbolic manipulation of the gray-box model obtained. To do so, we recommend the use of a software like EcosimPro [41] as modeling and simulation environment.
- 6.1.
- Perform a degree of freedom analysis.
- 6.2.
- Look for algebraic loops.
- 6.3.
- Check the existence of high-index problems.

- Initialization of the model. Use a stationary point obtained by the real system.
- Validation of the model.
- 8.1.
- Qualitative validation. Check the transient response and robustness of the model for different inputs.
- 8.2.
- Quantitative validation. Compare the output of the obtained model with the real process. This has been done in a graphical and analytical way.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Notation of the Model

- Streams.
- Zone/Equipment.
- Split Range PI controller.
- Legislation.
- Identification models.

VARIABLES | ||
---|---|---|

Name | Description | Units |

1. STREAMS | ||

Magnitude | ||

H | Specific Enthalpy | kJ/kg |

P | Pressure | barA |

Q | Heat Flow | kJ/s |

T | Temperature | ${}^{\circ}\mathrm{C}$ |

W | Mass Flow | kg/s |

Element | ||

B | Beet | |

G | Natural Gas | |

S | Steam | |

W | Water | |

Equipment | ||

$Bo$ | BStOutilers | |

$By$ | Bypass Valve | |

$Re$ | Relief Valve | |

$Sa$ | Stturator | |

$St$ | Storage zone | |

$Tu$ | Turbines | |

Direction | ||

$In$ | Flow that goes into the specified zone | |

$Out$ | Flow that leaves the specified zone | |

2. PROCESS | ||

${E}_{p}$ | Power consumed by the main process | kW |

${E}_{Tu}$ | Power energy generated in turbines | kW |

${m}_{St}$ | Accumulated mass beet in the storage zone | T |

${P}_{IV}$ | Pressure in the fourth effect of the evaporation | barA |

${Q}_{p}$ | Heat consumed by the main process | kW |

${\tau}_{St}$ | Beet residence time in storage zone | h |

Name | Description | Units |

3. SPLIT RANGE PI CONTROLLER | ||

$A{p}_{By}$ | Opening of the bypass valve | % |

$A{p}_{Re}$ | Opening of the relief valve | % |

e | Error | barA |

${P}_{SSaOutRef}$ | Pressure set-point | barA |

v | Output signal | % |

${v}_{i}$ | Integral action | % |

4. LEGISLATION | ||

${E}_{CHP}$ | Power generated in cogeneration mode | kW |

${E}_{plant}$ | Power generated in turbines | kW |

${F}_{CHP}$ | Energy obtained from fuel in cogeneration mode | kJ/s |

${F}_{plant}$ | Energy obtained from fuel | kJ/s |

$\mu {E}_{CHP}$ | Power efficiency of the CHP | % |

${\mu}_{G}$ | Global efficiency | % |

$\mu {Q}_{CHP}$ | Heat efficiency of the CHP | % |

$PES$ | Primary Saving Energy index | |

${Q}_{CHP}$ | Heat generated in cogeneration mode | kJ/s |

5. IDENTIFICATION MODELS | ||

$\Delta Var$ | Increase in the value of the variable with respect to the equilibrium point | |

$Va{r}_{xn}$ | nth internal state of the variable |

PARAMETERS | |||
---|---|---|---|

Name | Description | Value | Units |

${E}_{{p}_{eq}}$ | Value of ${E}_{p}$ at the identification point | 7769.26 | kW |

${H}_{WBo}$ | Specific enthalpy of the water used in the boilers | 550.52 | kJ/kg |

${H}_{WSa}$ | Specific enthalpy of the water used in the saturator | 125.80 | kJ/kg |

k | Polytropic index | 1.20 | |

$kp$ | Proportional gain | 140 | %/bar |

$K{v}_{By}$ | Bypass rated valve coefficient | 0.50 | kg/(s$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$bar) |

$K{v}_{Re}$ | Relief rated valve coefficient | 5.00 | kg/(s$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$bar) |

${K}_{Tu}$ | Turbines experimental parameter | 23.35 | (kg/s$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{}^{\circ}\mathrm{C}$)/ bar |

$\mu {E}_{Ref}$ | Reference cogeneration power efficiency | 0.53 | |

$\mu {Q}_{Ref}$ | Reference cogeneration heat efficiency | 0.87 | |

${\mu}_{Tu}$ | Efficiency of the steam turbine | 0.95 | |

${P}_{atm}$ | Atmospheric pressure | 1.00 | barA |

${P}_{I{V}_{eq}}$ | Value of ${P}_{IV}$ at the identification point | 1.28 | barA |

${P}_{SBo}$ | Steam Pressure at the output of the boilers | 37.30 | barA |

${P}_{SSaOu{t}_{eq}}$ | Value of ${P}_{SSaOut}$ at the identification point | 2.40 | barA |

$PC{I}_{G}$ | Natural Gas Lower Heating Value (LHV) | 48,130.09 | kJ/kg |

$PC{S}_{G}$ | Natural Gas Higher Heating Value (HHV) | 52,200 | kJ/kg |

$P{r}_{G}$ | Natural Gas Price | /kWh | |

$P{r}_{E}$ | Electricity Price | /kWh | |

${\rho}_{G}$ | Natural Gas density for the input conditions | 3.65 | kg/m${}^{3}$ |

${Q}_{{p}_{eq}}$ | Value of ${Q}_{p}$ at the identification point | 67,779.55 | kW |

${Q}_{SB{o}_{eq}}$ | Value of ${Q}_{SBo}$ at the identification point | 75,590.83 | kW |

$Ti$ | Integral gain | 10.00 | s |

${T}_{N}$ | Predicted horizon time | s | |

${v}_{max}$ | Maximum output signal of the splite range controller | 100.00 | % |

${W}_{BStOu{t}_{eq}}$ | Value of ${W}_{BStOut}$ at the identification point | 400.00 | T/h |

${W}_{BStIn}$ | Arrival of beet to the storage zone | 400.00 | T/h |

${W}_{N{G}_{eq}}$ | Value of ${W}_{G}$ at the identification point | 1.39 | kg/s |

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**Figure 2.**Dynamic response of ${Q}_{p}$. (

**a**) Dynamic response of ${Q}_{p}$ for a step in ${W}_{BStOut}$; (

**b**) Dynamic response of ${Q}_{p}$ for a step in ${P}_{SSaOut}$.

**Figure 3.**Experiments carried out to show linearity dependence between ${Q}_{p}$ and ${W}_{BStOut}$ (

**left**) and ${P}_{SSaOut}$ (

**right**).

**Figure 5.**Dynamic response of ${P}_{IV}$. (

**a**) Dynamic response of ${P}_{IV}$ for a step in ${W}_{BStOut}$; (

**b**) Dynamic response of ${P}_{IV}$ for a step in ${P}_{SSaOut}$.

**Figure 6.**Experiments carried out to show linearity dependence between ${P}_{IV}$ and ${W}_{BStOut}$ (

**left**) and ${P}_{SSaOut}$ (

**right**).

Simulator | Optimization Model | |
---|---|---|

Number of equations | 6485 | 52 |

- Static | 6036 | 38 |

- Dynamic | 449 | 14 |

Parameters | 2131 | 23 |

Variables | 6456 | 48 |

Input variables | 29 | 4 |

Non-linear algebraic loops | 8 | 3 |

Output Variable | RMSE [Ud] | Output Mean [Ud] | Relative Error [%] |
---|---|---|---|

${Q}_{p}$ | 566.03 kW | 67,614.00 kW | 0.84 |

${E}_{p}$ | 36.72 kW | 7793.89 kW | 0.47 |

${W}_{G}$ | 0.018 kg/s | 1.47 kg/s | 1.24 |

${\tau}_{St}$ | 0.52 h | 45.96 h | 1.12 |

PES | 0.01 | 0.13 | 6.31 |

${P}_{IV}$ | 0.01 barA | 1.22 barA | 0.52 |

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**MDPI and ACS Style**

Pablos, C.; Merino, A.; Acebes, L.F.
Modeling On-Site Combined Heat and Power Systems Coupled to Main Process Operation. *Processes* **2019**, *7*, 218.
https://doi.org/10.3390/pr7040218

**AMA Style**

Pablos C, Merino A, Acebes LF.
Modeling On-Site Combined Heat and Power Systems Coupled to Main Process Operation. *Processes*. 2019; 7(4):218.
https://doi.org/10.3390/pr7040218

**Chicago/Turabian Style**

Pablos, Cristian, Alejandro Merino, and Luis Felipe Acebes.
2019. "Modeling On-Site Combined Heat and Power Systems Coupled to Main Process Operation" *Processes* 7, no. 4: 218.
https://doi.org/10.3390/pr7040218