#
Home Energy Management System Incorporating Heat Pump Using Real Measured Data^{ †}

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

_{2}emissions. This paper presents a program for a HEMS using a Particle Swarm Optimisation (PSO) algorithm. A HP is used as the load and the aim of the optimisation program is to minimise the operational cost, i.e., the cost of electricity, while maintaining end-user comfort levels. This paper also details an indoor thermal model for temperature update in the heat pump control program. Real measured data from the UK Government’s Renewable Heat Premium Payment (RHPP) scheme was utilised to generate characteristic curves and equations that can represent the data. This paper compares different PSO variants with standard PSO and the unscheduled case calculated from the data for five winter days in 2019. Among all chosen algorithms, the Crossover Subswarm PSO (CSPSO) achieved an average saving of 25.61% compared with the cost calculated from the measured data with a short search time of 1576 ms for each subswarm. It is clear from this work that there is significant scope to reduce the cost of operating a HP while maintaining end user comfort levels.

## 1. Introduction

_{2}emission reduction [21]. There are two parts of this work. In the first part, the operation of the Combined Heat and Power CHP, Photovoltaic and storage system were optimised under changing electricity price. The second part investigated how to perform optimal load management in the proposed residential energy hub model. In order to achieve this, the modelling of a HP water heater was considered. The results also indicated that CO

_{2}signal is able to encourage end users to shift or reduce loads during peak hours and reduce the electricity cost and carbon emissions.

## 2. Materials and Methods

#### 2.1. Heat Pump Overview

_{2}emissions [4]. The CO

_{2}emissions when the HP is operating depend on the COP of the HP and the CO

_{2}emissions of electricity generation type from the utility company, i.e., where more renewable energy technologies are used for electricity generation, there are less CO

_{2}emissions. The CO

_{2}emissions of HPs are lower compared to other heating technology systems due to its high COP and can be further reduced under high renewable energy mix. A long term goal was set in the Paris Climate Change Conference 2015 for reduction of coal-fired power plants [25], which will decrease the CO

_{2}emissions for electricity generation and in turn reduce the CO

_{2}emissions during HP operation. Approximately 800,000 electrically driven HPs have been sold in the EU per year from 2010 to 2015 resulting in a total number of 7.5 million installed HPs [26]. By utilising a vapour compression cycle, the heat is taken from low-temperature sources like air, ground, lakes or sea water and released in residential houses by the HP at a higher temperature for space heating and/or hot water usage. It is indicated by Chua et al. [27] that with the development of HP technology, has resulted in an increase in the COP. Additionally, it is indicated by the simulated results of a German renewable energy system that the HP significantly reduced the CO

_{2}emissions compared to other energy sources [28,29]. Cockroft and Kelly investigated the potential of CO

_{2}emission reduction of air source HPs in a simulation for the UK in a 2050 scenario [30]. They concluded that comparing with stirling engine micro-Combined Heat and Power devices (CHP), Internal Combustion Engine (ICE) micro-CHP devices and fuel cells, the potential of CO

_{2}emission reduction of air source HPs is the greatest compared to using a condensing boiler and grid electricity.

#### 2.2. Particle Swarm Optimisation Overview

^{th}particle of N particles in the swarm and j represents the j

^{th}dimension of the D dimensional search space. t is the current number of iterations. v and x are the velocity and position of the particle respectively. p

_{ij}is the personal best position of a particle. p

_{gi}is the global best position of the swarm. r

_{1}and r

_{2}are two random functions in the range from zero to one. It can be seen from Equations (1) and (2) that the new position of a particle is determined by the velocity of the particle, which is affected by three terms. The first term is the current velocity of the particle which is weighted by inertia weight, w, it represents the habit of movement of a particle and shows the trend for a particle to maintain its velocity in the previous iteration. The second term is the cognition part, which is weighted by the cognitive acceleration coefficient, c

_{1}. This term represents the memory of searches in previous iterations of a particle and indicates the trend for a particle to move towards its personal-best position. The third term weighted by the social acceleration coefficient, c

_{2}, is the social part, which represents the collaboration among the particles, and indicates the trend for a particle to move towards the global best position of the swarm. The inertial weight, w, can be used to control the global search capability. High values of w increase global search capability and low values increase local search capability. Usually, c

_{1}is set equal to c

_{2}to ensure the same influence of personal and global experience, so that a better solution can be obtained [23].

#### 2.3. Overview of Particle Swarm Optimisation Variants

#### 2.3.1. Crossover Subswarm PSO (CSPSO)

#### 2.3.2. Quantum Particle Swarm Optimisation (QPSO)

_{ij}and p

_{gi}are the personal best value of the particle and global best value of the swarm respectively. r

_{1}and r

_{2}are two random numbers that are uniformly distributed between zero and one. The local attractor, p, of the particle, i, stochastically exist in a hyper-rectangle with p

_{ij}and p

_{gi}being two ends of its diagonal. Len is the characteristic length of Delta potential well and can be calculated using Equation (4). Delta potential well is one of the paradigm potential field model in quantum mechanics [39]:

_{1}and r

_{2}are two random numbers that are uniformly distributed between zero and one. The algorithm of QPSO can be described as below:

- (1)
- Randomly initialise the particle swarm.
- (2)
- Determine the initial personal optimal and global optimal solution.
- (3)
- For each dimension of each particle calculate p and Len.
- (4)
- Update the position of each particle in the swarm.
- (5)
- Update personal optimal and global optimal solution.
- (6)
- Before the preset number of iterations is reached, repeat from step 3 to 5.

#### 2.3.3. Quantum Particle Swarm Optimisation Procedure with Lévy Flights (QPSOL)

_{i}is the particle position. λ

_{i}is a random number with Lévy distribution and β is the constriction coefficient that changes the step size of the flight.

#### 2.4. Derivation of Indoor Thermal Model

_{out}is set constant and the indoor temperature T

_{in}is uniform throughout the house. The indoor thermal model and its electrical equivalent model are given diagrammatically in Figure 1.

_{in}(°C), to the low temperature outdoor environment with low temperature, T

_{out}(°C). The rate of heat flow is q (kW).

_{in}and V

_{out}are the voltages (volt) above and below the capacitor. The discharging current is i (amp). The elapsed time is t (s).

_{in}is a function of time t:

#### 2.5. Measured Heat Pump Performance Data

#### 2.6. Program Description

^{2}. The typical U values for the walls, ceiling and windows are used to conduct calculations to UK standards. The result of overall thermal conductivity is 0.27 kW/°C. To validate the correctness of this value, simulations were conducted on the temperature update model i.e., Equation (10) using outdoor temperatures and the heat pump hourly heat output data for the chosen HP for a month between 3-1-2019 to 3-2-2019. A temperature of 18 °C is recommended by the 2016 Cold Weather Plan for England as day and night minimum temperature for those 65 and older or anyone with pre-existing medical conditions [56]. For houses insulated to typical UK levels, the on/off set-point for the heating system is usually between 19 to 23 °C [57]. Thus, the initial temperature at midnight is assumed to be 19 °C. When A is 0.27 kW/°C, among all indoor temperature data generated, most data are within the typical range of 19 to 23 °C [57]. Additionally, 2% of the data are above 23 °C but below 23.5 °C. No data are below 19 °C. Thus, all data generated are above the 18 °C which has been defined as the minimum temperature [56]. Therefore, this A value is considered suitable for a UK housing condition. The indoor temperatures on the chosen dates were then generated using the temperature update model assuming the initial temperature at midnight is 19 °C.

_{hp}. The final objective function is constructed as shown in Equation (13):

## 3. Results and Discussion

#### 3.1. The Results of the Standard Particle Swarm Optimisation

_{hp}, is shown in Figure 5.

_{hp}, gradually decreases from 1.261 when inertia weight w = 0.1 to the lowest value of 1.233 when inertia weight w = 0.8. When inertia weight w = 0.8, the total electricity cost after optimisation using standard PSO is compared with the actual electricity cost in the data. For the chosen data, the total electricity consumption for the HP during the 24 h on 3-2-2019 is €3.13. When inertia weight w = 0.8, the total electricity cost is €2.47. The saving is €0.66, which is 21.09% cost reduction compared with the actual cost in the data. The average search time of standard PSO is 1089 ms.

#### 3.2. The Results of the Crossover Subswarm PSO

_{hp}, which occurred when the number of subswarms is 50 and crossover rate, CR, is 0.3. Crossover is applied when personal best values haven’t changed for 10 iterations. 50 particles are used in each subswarm. The total electricity cost for the day is €2.28 which is €0.85 or 27.16% saving compared with the €3.13 cost in the data. The average search time of CSPSO for each subswarm is 1576 ms.

#### 3.3. The Results of the QPSO and QPSOL

_{hp}, when the total electricity cost is €2.25 and parameter $g$ is set to 0.9. The number of particles in each subswarm is 30. The number of subswarms is 50. Although the optimisation result of improved QPSO is slightly better than CSPSO, the search time of improved QPSO for each subswarm is 6400 ms, which is about four times CSPSO.

_{hp}, when the total electricity cost is €2.25. Index of stability, α, is 1.4 and constriction coefficient, β, is 0.6. The number of particles in each subswarm is 30. The number of subswarms is 60. Although the optimisation result of improved QPSOL is slightly better than CSPSO, the search time of improved QPSOL for each subswarm is 18252 ms, which is about 11 times CSPSO.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Coefficient of Performance (COP) versus outdoor temperature for a heat pump operating over a one-year period.

**Figure 3.**Heat pump hourly heat output versus outdoor temperature for a heat pump operating over a one-year period.

Data | 3rd Feb. | 31st Jan. | 23rd Jan. | 20th Jan. | 18th Jan. | Average |
---|---|---|---|---|---|---|

Optimised electricity cost (€) | 2.47 | 3.01 | 3.56 | 3.01 | 2.79 | |

Electricity cost in data (€) | 3.13 | 3.81 | 4.53 | 3.82 | 3.52 | |

Percentage of cost reduction (%) | 21.09 | 21.00 | 21.41 | 21.20 | 20.74 | 21.09 |

Data | 3rd Feb. | 31st Jan. | 23rd Jan. | 20th Jan. | 18th Jan. | Average |
---|---|---|---|---|---|---|

Optimised electricity cost (€) | 2.28 | 2.85 | 3.37 | 2.85 | 2.65 | |

Electricity cost in data (€) | 3.13 | 3.81 | 4.53 | 3.82 | 3.52 | |

Percentage of cost reduction (%) | 27.16 | 25.20 | 25.61 | 25.39 | 24.72 | 25.61 |

Data | 3rd Feb. | 31st Jan. | 23rd Jan. | 20th Jan. | 18th Jan. | Average |
---|---|---|---|---|---|---|

Optimised electricity cost (€) | 2.25 | 2.81 | 3.31 | 2.77 | 2.64 | |

Electricity cost in data (€) | 3.13 | 3.81 | 4.53 | 3.82 | 3.52 | |

Percentage of cost reduction (%) | 28.12 | 26.25 | 26.93 | 27.49 | 25.00 | 26.76 |

Data | 3rd Feb. | 31st Jan. | 23rd Jan. | 20th Jan. | 18th Jan. | Average |
---|---|---|---|---|---|---|

Optimised electricity cost (€) | 2.25 | 2.8 | 3.32 | 2.77 | 2.61 | |

Electricity cost in data (€) | 3.13 | 3.81 | 4.53 | 3.82 | 3.52 | |

Percentage of cost reduction (%) | 28.12 | 26.51 | 26.71 | 27.49 | 25.85 | 26.93 |

Standard PSO | CSPSO | Improved QPSO | Improved QPSOL | |
---|---|---|---|---|

Average percentage of cost reduction (%) | 21.09 | 25.61 | 26.76 | 26.93 |

Search time (ms) | 1089 | 1576 | 6400 | 18252 |

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## Share and Cite

**MDPI and ACS Style**

Cao, Z.; O’Rourke, F.; Lyons, W.; Han, X.
Home Energy Management System Incorporating Heat Pump Using Real Measured Data. *Sensors* **2019**, *19*, 2937.
https://doi.org/10.3390/s19132937

**AMA Style**

Cao Z, O’Rourke F, Lyons W, Han X.
Home Energy Management System Incorporating Heat Pump Using Real Measured Data. *Sensors*. 2019; 19(13):2937.
https://doi.org/10.3390/s19132937

**Chicago/Turabian Style**

Cao, Zhengnan, Fergal O’Rourke, William Lyons, and Xiaoqing Han.
2019. "Home Energy Management System Incorporating Heat Pump Using Real Measured Data" *Sensors* 19, no. 13: 2937.
https://doi.org/10.3390/s19132937