# Agent-Based Modeling of a Thermal Energy Transition in the Built Environment

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Definition of the Conceptual Framework

#### 2.1. Sociotechnical Systems (STS)

#### 2.2. Complex Adaptive Systems (CAS)

#### 2.3. Basic Notions of Agent-Based Modeling

## 3. Materials and Methods

#### 3.1. Model Development

#### 3.2. Computational Simulations

#### 3.3. Analysis of Results

## 4. Illustrative Example: from Natural Gas-Based to Natural Gas-Free Heating in Residential Neighborhoods

#### 4.1. The Thermal Energy Transition through the Lenses of STS and CAS

#### 4.2. Model Overview

- Under which socioeconomic conditions did the neighborhood transition fully to natural gas-free heating?
- What were the costs of the transition?
- Which changes in household insulation and heating systems took place during these transitions?

#### 4.2.1. Model Entities, State Variables, and Scale

- Equation (1) applies to technologies that consume natural gas and not electricity.
- In Equation (2), information regarding maintenance costs and investment costs is part of the environment and is available to agents.
- In Equation (3), annual demand is retrieved from the environment. See Appendix A, Table A3.
- In Equation (4), retail electricity or natural gas price of the present year are used, depending on the technology.
- In Equation (5), annual operation costs are retrieved from the environment. See Appendix A, Table A2.

- Business as usual (natural gas boiler and low insulation)
- Micro-CHP and low insulation
- Electric radiator and low insulation
- Aerial heat pump and low insulation
- Geothermal heat pump and low insulation
- Natural gas boiler and medium insulation
- Natural gas boiler and high insulation
- Micro-CHP and medium insulation
- Micro-CHP and high insulation
- Electric radiator and medium insulation
- Electric radiator and high insulation
- Aerial heat pump and medium insulation
- Aerial heat pump and high insulation
- Geothermal heat pump and medium insulation
- Geothermal heat pump and high insulation

#### 4.2.2. Process Overview and Scheduling

#### 4.3. Experimental Design

## 5. Results and Discussion from the Illustrative Example

#### 5.1. Modeling Question 1: Socioeconomic Conditions

#### 5.2. Modeling Question 2: Cost of the Transition

#### 5.3. Modeling Question 3: Changes in Technology and Insulation

#### 5.4. Integration and Discussion

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Additional Description of the ABM, Based on the ODD Protocol

#### Appendix A.1. Design Concepts

- Basic principle: The neighborhood’s cumulative costs and annual natural gas consumption results from individual decisions of households to use and replace their technology. Those decisions are based on some of agents’ state variables and external factors.
- Emergence: The neighborhood’s cumulative costs, annual natural gas consumption, number of heating systems of each type, and insulation levels.
- Adaptation: While households use current retail energy prices to select the heating system and insulation level that best meets their objectives, their state variables HRZ, ORI, THR, and ACCI remain constant during a simulation run.
- Objectives: Households are either natural gas minimizers (environmentally oriented) or cumulative cost minimizers (financially and socially oriented). Socially-oriented agents act only if a fraction of their peers has acted.
- Learning/prediction: Households do not use learning mechanisms nor forecasting. They assume that the current retail energy prices will remain constant.
- Sensing: Households are assumed to know the present price of heating systems, insulation levels, electricity and natural gas, and the number of heating systems of each type, and insulation levels in the neighborhood by the end of the previous year.
- Interaction: Socially-oriented households consider replacing their heating systems or improving their insulation only when a fraction of their peers has also made changes.
- Stochasticity: While the model is initialized stochastically, all properties of households but one are assigned deterministically (value orientation: ORI). Therefore, households are identical except for their value orientation. As a result, stochastic initialization does not have an effect on model outcomes.
- Collectives: The model does not account for aggregations between households. An example of aggregation would be multiple households investing together in one heating system to meet their heat demand.
- Observation: The neighborhood’s cumulative costs, annual natural gas consumption, number of heating systems of each type, and insulation levels are the variables used for observing system level behavior.

#### Appendix A.2. Initialization

#### Appendix A.3. Input Data

Parameter | Value | Source |
---|---|---|

Retail natural gas prices for the first year [Euro/kWh] | 0.08 | Based on [50] |

Retail electricity prices for the first year [Euro/kWh] | 0.16 | Based on [51] |

**Table A2.**Input data for technologies, per technology: Natural gas boiler, micro-CHP, electric radiators, aerial heat pumps, and geothermal heat pumps.

Parameter | Value for Each Type of Technology | Source |
---|---|---|

Thermal efficiency [dmnl] | 1, 0.60, 1, 2.6, 3.3 | Assumptions and [49] |

Electrical efficiency [dmnl] | 0, 0.28, 0, 0, 0 | Assumptions and [49] |

Capital costs [€/kW] | 0, 2100, 300, 1130, 1675 | Assumptions and [49] |

Annual operation costs [€ per kw/year] | 11.18, 42, 10, 22.6, 33.5 | Assumptions and [49] |

Parameter | Value for Each Level | Source |
---|---|---|

Capacity required from a technology to meet demand [kW] | 15, 8, 5 | Assumptions |

Capital costs when dwellings have low level [€] | NA *, 5500, 10000 | Assumptions |

Capital costs when dwellings have medium level [€] | NA *, NA *, 6000 | Assumptions |

Heat demand [kWh] | 25000, 10000, 5000 | Assumptions |

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**Figure 1.**Scatterplot of cumulative costs of energy and technologies in the neighborhood as a function of natural gas consumed in year 20, for all-simulation-runs. A single dot may represent multiple dots that overlap.

**Figure 2.**Boxplots of natural gas consumed by the neighborhood in year 20 in all-simulation-runs, classified in population groups according to value orientation. PopORI: 1 = [0.33, 0.33, 0.33], 2 = [0.50, 0.25, 0.25], 3 = [0.25, 0.50, 0.25], 4 = [0.25, 0.25, 0.50], 5 = [1, 0, 0], 6 = [0, 1, 0], 7 = [0, 0, 1].

**Figure 3.**Cumulative costs by the neighborhood in year 20, for all-simulation-runs, classified in gas-dependent and gas-free.

**Figure 4.**Cumulative costs of the transition: Gas-free-subset, grouped by (

**a**) popORI; (

**b**) popACCI, and (

**c**) popHRZ.

**Figure 6.**Cumulative costs of the transition (gas-free-subset). Each plot displays results from simulation runs with a unique combination of popACCI (grey labels on top of each column) and popORI (grey labels to the right of each row). In each plot, a boxplot is displayed for simulation runs with the same popHRZ, e.g., the plot in the top right corner displays simulation runs in which popACCI = 1.00 and popORI = 1, the first boxplot corresponds to popHRZ = 5, and the second one, to popHRZ = 10.

**Figure 7.**Heating system pathways of the gas-free-subset, classified by popHRZ (grey labels on top of each column) and a unique combination of dgp, popACCI, and dep (labels in the right side of each row). Each line plot shows the number of dwellings with each heating system over time. Blue frames indicate pathways from simulation runs where popORI = 1, 2, 3, 4, 5, or 7. Each plot without a blue frame contains only the pathway for popORI = 5. Black frames indicate pathways in which agents invested in heating systems more than one time during the simulation run.

**Figure 8.**Insulation pathways of the gas-free-subset, classified by popHRZ (grey labels on top of each column) and a unique combination of dgp, popACCI, and dep (labels in the right side of each row). Each line plot shows the number of dwellings with each insulation level over time. Blue frames indicate pathways from simulation runs where popORI = 1, 2, 3, 4, 5, or 7. Each plot without a blue frame contains only the pathway for popORI = 5.

**Figure 9.**Pathways of the gas-free-subset when popHRZ = 5 or 10, dgp = 0.04, and dep = −0.04, classified by popHRZ (grey labels on top of each column) and a unique combination of popORI and popACCI (labels in the right side of each row). Each line plot shows the number of dwellings with each heating system over time (

**a**) or with each insulation level over time; (

**b**). These plots are a zoom-in on the content of the blue frames in Figure 7 and Figure 8.

Variable | Units | Description | Possible Values |
---|---|---|---|

Insulation level | Dimensionless | Insulation level of a dwelling | Low, Medium or High |

Heating system | Dimensionless | Type of heating system | Natural gas boiler, electric radiator, micro-CHP, aerial heat pump, geothermal heat pump |

Annual natural gas consumption | [MWh] | Gas consumption in one year | Positive real numbers |

Cumulative costs | Thousands of Euros | Investment, maintenance and operation costs | Positive real numbers |

HRZ | Years | Time horizon | Positive integers |

INV | Years | Indicates the number of years left before a time equal to the agent’s HRZ has passed since the agent’s last investment | Positive integers |

ORI | Dimensionless | Value orientation | Environmental, Social, Financial |

THR | Dimensionless | Threshold after which socially oriented agents will make a decision | 0 ≤ Fraction ≤ 1 |

ACCI | Dimensionless | Ability to compare combined investments | 0 ≤ Fraction ≤ 1 |

Variable | Units | Description | Possible Values |
---|---|---|---|

dgp | %/year | Annual percentage change in the retail natural gas price | Real numbers |

dep | %/year | Annual percentage change in the retail electricity price | Real numbers |

popACCI | Dimensionless | Fraction of households in the population that is able to compare combined investments. | 0 ≤ Fraction ≤ 1 |

popHRZ | Dimensionless | Time horizon shared by all households in the population, in years. | Positive integers |

popORI | Dimensionless | Fraction of households in the population with each value orientation: Environmental (Env), social (Soc) and financial (Fin). | 0 ≤ Env, Soc, Fin ≤ 1 [Env, Soc, Fin] Env + Soc + Fin = 1 |

Type of Variation | Groups of Variations |
---|---|

dgp | −0.04, 0, 0.04 |

dep | −0.04, 0, 0.04 |

popORI | 1 = [0.33, 0.33, 0.33] 2 = [0.50, 0.25, 0.25] 3 = [0.25, 0.50, 0.25] 4 = [0.25, 0.25, 0.50] 5 = [1, 0, 0] 6 = [0, 1, 0] 7 = [0, 0, 1] |

popACCI | 0 and 1 |

popHRZ | 1, 5, 10, 15, 20, 30 |

Subset | Number of Scenarios | Definition |
---|---|---|

All-simulation-runs | 756 | Results from all simulation runs. |

Gas-dependent-subset | 628 | Subset of all-simulation-runs in which the neighborhood consumed natural gas in year 20, and thus did not achieve the transition to a gas-free neighborhood. |

Gas-free-subset | 128 | Subset of all-simulation-runs in which did not consume natural gas in year 20, and thus fully achieved the thermal energy transition to a gas-free neighborhood. |

**Table 5.**Sets of sufficient scenario conditions for simulation runs to be part of the gas-free-subset.

Type of Variation | Set 1 | Set 2 |
---|---|---|

popORI | 5 | 1, 2, 3, 4, 7 |

popHRZ | - | 5, 10 |

dgp | - | increasing |

dep | - | decreasing |

Group | Number of Scenarios | Mean | Standard Deviation | Median | IQR * |
---|---|---|---|---|---|

All-simulation-runs | 756 | 1238 | 640 | 1040 | 760 |

Gas-dependent-subset | 628 | 1105 | 420 | 1040 | 676 |

Gas-free-subset | 128 | 1889 | 1027 | 1495 | 2126 |

**Table 7.**Results from statistical tests for all-simulation-runs, grouped as gas-free or gas-dependent.

Test | Results | Conclusion |
---|---|---|

Wilcoxon rank sum test | W = 22403 p-value = 2.745e-15 | Groups’ medians are significantly different |

Shapiro-Wilk normality test | W = 0.96395 p-value = 1.077e-12 | Sample deviates from normality |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Nava Guerrero, G.d.C.; Korevaar, G.; Hansen, H.H.; Lukszo, Z.
Agent-Based Modeling of a Thermal Energy Transition in the Built Environment. *Energies* **2019**, *12*, 856.
https://doi.org/10.3390/en12050856

**AMA Style**

Nava Guerrero GdC, Korevaar G, Hansen HH, Lukszo Z.
Agent-Based Modeling of a Thermal Energy Transition in the Built Environment. *Energies*. 2019; 12(5):856.
https://doi.org/10.3390/en12050856

**Chicago/Turabian Style**

Nava Guerrero, Graciela del Carmen, Gijsbert Korevaar, Helle Hvid Hansen, and Zofia Lukszo.
2019. "Agent-Based Modeling of a Thermal Energy Transition in the Built Environment" *Energies* 12, no. 5: 856.
https://doi.org/10.3390/en12050856