A New Solar Assisted Heat Pump System with Underground Energy Storage: Modelling and Optimisation
Abstract
:1. Introduction
2. A Heating System Based on a Photovoltaic Panel and a Solar Collector
2.1. Process Description
2.2. Comparison with Other Systems
2.3. Process Modelling
- D is the tank diameter (3 m);
- L is length of the tank (10 m);
- and are ground heat transfer to the first and the second tank, respectively;
- is heat transferred through the heat pump to the building;
- is solar heat flow from PVT panels cooling;
- is solar heat flow from solar collectors;
- , are water temperatures in the storages tanks 1 and 2, respectively;
- is specific heat of water;
- is the ratio of heat taken from the tank 1 to the entire heat taken by the heat pump;
- is density of water.
- is the total height of the domain assumed as 13 m;
- is the yearly average ground temperature, assumed to be equal to 7.5 ;
- is the ground temperature, the initial ground temperature is assumed to be equal to 20 ;
- is the overall heat transfer coefficient from the ground top layer to the external environment, equal to ;
- W is the width of the domain, assumed as 10 m;
- c is specific heat capacity of the ground;
- and are the heat transfer coefficients from the tank 1 and tank 2, respectively;
- k is thermal conductivity of the ground;
- x and y are Cartesian coordinates;
- is density of the ground.
2.4. Optimisation Objective
- To use less electrical energy due to the increase in the overall COP of the heat pump;
- To use mostly the underground energy storage unit instead of a borehole heat exchanger to allow efficient ground regeneration.
3. Optimisation Methods Used
3.1. Gradient-Based Optimisation Algorithm
3.2. Genetic Algorithm
3.3. Particle Swarm Optimisation Algorithm
3.4. Jaya Algorithm
4. Results of Simulations
- In spite of the fact that in the gradient-based SQP algorithm relatively high number of iterations is used, it gives the worst results. Probably, the obtained results are shallow local minima.
- All three tested heuristic optimisation methods give better results than the SQP one.
- The PSO algorithm is the worst one in the group of the heuristic optimisation methods. Numerous attempts have been made to improve the results by using a larger population of individuals or by increasing the number of possible iterations, but such approaches do not lead to any better results. Typically, after some 50–80% of the allowed iterations, the optimised cost-function is practically constant and calculations are terminated.
- In comparison with the PSO algorithm, better results, in particular for the sampling time equal to 24 h, 12 h, or 6 h, are obtained by the genetic algorithm, although we may observe that as the sampling time is reduced, the genetic algorithm gives worse results. For the sampling time equal to 3 h, 2 h, or 1 h, the obtained results are only slightly better than those obtained by the PSO algorithm. Similarly to the PSO algorithm, also in the case of the genetic algorithm, increasing the number of individuals or the number of possible iterations does not yield better results.
- Generally, the Jaya algorithm gives the best results, the only exception is for = 24 h in which the genetic algorithm is better, but the difference is really insignificant.
- It is important that the Jaya algorithm finds good solutions for all tested values of the sampling time , which is not true in the case of the second-best approach, i.e., the genetic algorithm.
- As far as heuristic optimisation algorithms are concerned, the presented results have been achieved for exactly the same number of maximal iterations (as specified in Table 2 for the consecutive values of the sampling time , the only exception is for the sampling time 1 h, the Jaya algorithm needs a lower number of iterations) and population size (30 individuals).
- Decreasing the sampling instant leads to increasing the number of decision variables in the optimization problem. The more the decision variables, the more difficult the optimization task. Hence, more iterations of the optimization algorithms are necessary as shown in Table 2. It greatly increases the resulting calculation time.
- Since decreasing the sampling time does not improve the final value of the cost-function but only makes calculations more time-consuming, it is recommended to use quite long sampling periods, e.g., 24 h or 12 h.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Acronyms
COP | Coefficient Of Performance |
DHW | Domestic Hot Water |
GA | Genetic Algorithm |
MPC | Model Predictive Control |
PSO | Particle Swarm Optimisation |
PVT | Photovoltaic Thermal Hybrid Solar Panels |
RES | Renewable Energy Sources |
SAGSHP | Solar-Assisted Ground Source Heat Pump |
SQP | Sequential Quadratic Programming |
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Month | Monthly Averaged Daily Solar Irradiation Flux | Irradiation Hours |
---|---|---|
January | 400 | 2.8 |
February | 400 | 3.6 |
March | 500 | 4.8 |
April | 600 | 7 |
May | 800 | 7.7 |
June | 800 | 7.9 |
July | 900 | 8.8 |
August | 900 | 7.5 |
September | 700 | 6.1 |
October | 500 | 4.8 |
November | 400 | 3.4 |
December | 400 | 2.5 |
SQP Algorithm | PSO Algorithm | Genetic Algorithm | Jaya Algorithm | |
---|---|---|---|---|
24 h | 200 | 500 | 500 | 500 |
12 h | 200 | 1000 | 1000 | 1000 |
6 h | 300 | 1500 | 1500 | 1500 |
3 h | 500 | 2000 | 2000 | 2000 |
2 h | 500 | 2500 | 2500 | 2500 |
1 h | 700 | 3000 | 3000 | 2500 |
SQP Algorithm | PSO Algorithm | Genetic Algorithm | Jaya Algorithm | |
---|---|---|---|---|
24 h | 0.8984 | 0.9045 | 0.9328 | 0.9318 |
12 h | 0.8986 | 0.9033 | 0.9289 | 0.9330 |
6 h | 0.8984 | 0.9018 | 0.9192 | 0.9317 |
3 h | 0.8984 | 0.9006 | 0.9054 | 0.9298 |
2 h | 0.8982 | 0.8997 | 0.9046 | 0.9306 |
1 h | 0.8984 | 0.9000 | 0.9035 | 0.9280 |
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Ocłoń, P.; Ławryńczuk, M.; Czamara, M. A New Solar Assisted Heat Pump System with Underground Energy Storage: Modelling and Optimisation. Energies 2021, 14, 5137. https://doi.org/10.3390/en14165137
Ocłoń P, Ławryńczuk M, Czamara M. A New Solar Assisted Heat Pump System with Underground Energy Storage: Modelling and Optimisation. Energies. 2021; 14(16):5137. https://doi.org/10.3390/en14165137
Chicago/Turabian StyleOcłoń, Paweł, Maciej Ławryńczuk, and Marek Czamara. 2021. "A New Solar Assisted Heat Pump System with Underground Energy Storage: Modelling and Optimisation" Energies 14, no. 16: 5137. https://doi.org/10.3390/en14165137
APA StyleOcłoń, P., Ławryńczuk, M., & Czamara, M. (2021). A New Solar Assisted Heat Pump System with Underground Energy Storage: Modelling and Optimisation. Energies, 14(16), 5137. https://doi.org/10.3390/en14165137