# Investigation of Heat Pump Operation Strategies with Thermal Storage in Heating Conditions

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## Abstract

**:**

## 1. Introduction

## 2. System Simulation Model

#### 2.1. Target System

#### 2.2. Control Mode Simulation Model

## 3. Control Simulation Results

#### 3.1. Comparison of Simulation and Experiment

#### 3.2. Winter Simulation Results

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

${A}_{p}$ | Heat transfer area of PCM (m^{2}) |

${C}_{p,w}$ | Specific heat of water (kJ/kg·K) |

${C}_{p,p}$ | Specific heat of PCM (kJ/kg·K) |

${C}_{pc,l}$ | Liquid state cooling PCM specific heat (kJ/kg·K) |

${C}_{ph,l}$ | Liquid state heating PCM specific heat (kJ/kg·K) |

${C}_{ph,s}$ | Solid state heating PCM specific heat (kJ/kg·K) |

$COP$ | Coefficient of performance (-) |

$CO{P}_{n}$ | Normalized coefficient of performance (-) |

$Cos{t}_{tot}$ | Total electricity cost (₩) |

$Cos{t}_{d}$ | Daytime electricity cost (₩) |

$Cos{t}_{m}$ | Nighttime electricity cost (₩) |

$D$ | PCM pack interval inside the thermal storage tank (m) |

${F}_{PLR}$ | Correction factor for part load power consumption (-) |

${h}_{fg}$ | Enthalpy of water for latent processes (kJ/kg) |

${h}_{SPF}$ | Convection heat transfer coefficient according to SPF (kW/m^{2}·K) |

${h}_{w}$ | Convection heat transfer coefficient of water (-) |

$i$ | Time step index (-) |

$j$ | Position step index (-) |

$k$ | Position step index (-) |

${k}_{w}$ | Conduction heat transfer coefficient of water (-) |

$L$ | Distance from the top to the control volume in the height direction (m) |

${M}_{pc}$ | Mass of cooling PCM (kg) |

${M}_{ph}$ | Mass of heating PCM (kg) |

${\dot{m}}_{w}$ | Mass flow rate of water (kg/s) |

${M}_{w}$ | Mass of water (kg) |

${M}_{SPF}$ | Weight of solidified PCM (kg) |

$\mu $ | Viscosity coefficient of water (N·s/m^{2}) |

$Nu$ | Nusselt number, $Nu={h}_{w}D/{k}_{w}$ (-) |

$PLR$ | Part load ratio (-) |

$Pr$ | Prandtl number, $Pr={C}_{p,w}\mu /{k}_{w}$ (-) |

$\dot{Q}$ | Heat capacity (kW) |

${Q}_{p,lat}$ | Total latent heat capacity of PCM (kJ) |

${Q}_{p,sen}$ | Total sensible heat capacity of PCM (kJ) |

$\dot{{Q}_{R}}$ | Reference load capacity (kW) |

$\dot{{Q}_{F}}$ | Full-load capacity (kW) |

${\dot{Q}}_{ht}$ | Capacity of heat pump (kW) |

${\dot{Q}}_{ht,ful}$ | Full-load capacity of heat pump (kW) |

${\dot{Q}}_{ht,opt}$ | Optimum capacity of heat pump (kW) |

${\dot{Q}}_{load}$ | Load of the building (kW) |

${Q}_{load}$ | Total load of the building (kJ) |

${\dot{Q}}_{st}$ | Capacity of thermal storage (kW) |

${Q}_{st}$ | Total accumulated Capacity of thermal storage (kJ) |

${\dot{Q}}_{st,ref}$ | Reference capacity of thermal storage (kW) |

${Q}_{w,sen}$ | Total sensible heat capacity of water (kJ) |

${Q}_{p,sen}$ | Total sensible heat capacity of PCM (kJ) |

${Q}_{p,lat}$ | Total latent heat capacity of PCM (kJ) |

$R$ | Variable of minimum cost (₩) |

$Re$ | Reynolds number, $Re=VD/v$ (-) |

$SPF$ | Solid packing factor (%) |

${T}_{c}$ | Outlet temperature of water for heat pump model (°C) |

${T}_{e}$ | Outdoor temperature for heat pump model (°C) |

${T}_{w}$ | Water temperature at control volume (°C) |

${T}_{p}$ | PCM temperature at control volume (°C) |

${T}_{pc}$ | Cooling PCM temperature at control volume (°C) |

${T}_{pc,l}$ | Liquid state Cooling PCM temperature (°C) |

${T}_{ph}$ | Heating PCM temperature at control volume (°C) |

${T}_{in}$ | Inlet water temperature at control volume (°C) |

${T}_{out}$ | Outlet water temperature at control volume (°C) |

${T}_{ht,i}$ | Inlet water temperature of heat pump (°C) |

${T}_{ht,o}$ | Outlet water temperature of heat pump (°C) |

$\xb7{T}_{st}$ | Temperature change of thermal storage tank during discharging process (°C) |

${t}_{1}$ | Daytime operating time (-) |

${t}_{2}$ | Nighttime operating time (-) |

${U}_{s}$ | Overall heat transfer coefficient of the sensible process (kW/m^{2}·K) |

${U}_{l}$ | Overall heat transfer coefficient of the latent process (kW/m^{2}·K) |

$v$ | Kinematic viscosity of water in the control volume (m/s) |

$V$ | Flow rate of water in the control volume (m/s) |

${V}_{w,cv}$ | Volume of water at control volume (m^{3}) |

${V}_{p,cv}$ | Volume of PCM at control volume (m^{3}) |

$\dot{W}$ | Power consumption (kW) |

$\dot{{W}_{R}}$ | Reference power consumption (kW) |

$\dot{{W}_{F}}$ | Full-load power consumption (kW) |

${W}_{p}$ | Predicted power consumption (-) |

${x}_{st}$ | Normalized accumulated heat capacity (-) |

${\rho}_{w}$ | Density of water (kg/m^{3}) |

${\rho}_{p}$ | Density of PCM (kg/m^{3}) |

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**Figure 2.**PCM (Phase change material) samples and thermal storage tank schematic for heating system: (

**a**) picture of packed PCMs for cooling and heating (left: cooling; right: heating); and (

**b**) schematic of thermal storage tank.

**Figure 4.**Comparison between the experiment and the simulation results of heat charging process and heat discharging process for 10 h.

**Figure 5.**Comparison between the experiment and the simulation results: (

**a**) comparison of time step in 5 h instant of charging process; and (

**b**) comparison of control volume layers in 5 h instant of charging process.

**Figure 7.**Performance of heat pump according to PLR (Part load ratio): (

**a**) correction factor models for power consumption of heat pump under part load operation; and (

**b**) the normalized COP (Coefficient of performance) of heat pump according to part load ratio.

**Figure 9.**Conceptual diagram of conventional control methods: (

**a**) thermal storage priority method; and (

**b**) heat pump priority method.

**Figure 14.**Analysis of heating load and heating capacity: (

**a**) percentage of winter season and average outdoor temperature by each heating load; and (

**b**) heating capacity rate due to normalized loads with over 80% load.

**Figure 15.**Performance analysis by control method: (

**a**) the normalized COP by control mode according to capacity ratio of heat pump; and (

**b**) the normalized COP by control mode according to heating load rate.

**Figure 16.**Power consumption and electricity cost analysis by control method: (

**a**) normalized power consumption by thermal storage priority method according to load size; and (

**b**) normalized electricity cost by thermal storage priority method according to load size.

Parameter | Specification | |
---|---|---|

Type | Heating | Cooling |

Thermal Conductivity of liquid (W/m·K) | 0.167 | 0.136 |

Thermal Conductivity of solid (W/m·K) | 0.346 | 0.307 |

Average phase change temperature (°C) | 52 | 4 |

Heat of fusion (kJ/kg) | 196.87 | 252.30 |

Specific heat of liquid (kJ/kg·K) | 1.97 | 2.07 |

Specific heat of solid (kJ/kg·K) | 2.30 | 2.32 |

Size (mm) | 17.3 (W) × 250 (L) × 310 (H) | |

Pack weight (kg) | 1 |

Parameter | Specification | |
---|---|---|

Type | Heating | Cooling |

Packed PCM (EA) | 147 | 1197 |

Latent thermal storage energy (kJ) | 28,940 | 302,000 |

Total thermal storage energy (kJ) | 288,000 | 483,000 |

Operating temperature range (°C) | 40–55 | 2–12 |

Size (mm) | 1750 (W) × 2000 (L) × 2000 (H) | |

Volume (m^{3}) | 5.616 |

Coefficient | ${\mathit{a}}_{\mathbf{1}}$ | ${\mathit{a}}_{\mathbf{2}}$ | ${\mathit{a}}_{\mathbf{3}}$ | ${\mathit{a}}_{\mathbf{4}}$ | ${\mathit{a}}_{\mathbf{5}}$ |
---|---|---|---|---|---|

Charging | 51 | 0.5 | −154 | 235 | −121 |

Discharging | 5 | 141 | −300 | 370 | −143 |

Parameter | Condition Range |
---|---|

Tc (°C) | 55, 52, 48, 43, 40 |

Te (°C) | 5, 1, −5, −11, −15 |

Load (kW) | 10, 25, 50 ,75, 100 |

Water flow rate (lpm) | 7 |

Coefficient | Parameter | |||||
---|---|---|---|---|---|---|

Heat capacity | ${b}_{1}$ | ${b}_{2}$ | ${b}_{3}$ | ${b}_{4}$ | ${b}_{5}$ | ${b}_{6}$ |

25.59 | −0.0788 | −0.4708 | −0.0058 | 0.0030 | 0.0029 | |

Power consumption | ${c}_{1}$ | ${c}_{2}$ | ${c}_{3}$ | ${c}_{4}$ | ${c}_{5}$ | ${c}_{6}$ |

1.2850 | −0.0622 | 0.0591 | −0.0003 | −0.0001 | 0.0001 | |

Factor for part load power consumption | ${d}_{1}$ | ${d}_{2}$ | ${d}_{3}$ | |||

0.7558 | −0.2237 | 0.4578 |

**Table 6.**Zone electric rate based on daytime and nighttime electric power rate by KEPCO (Korea Electric Power Corporation).

Parameter | Time | Electricity Rate |
---|---|---|

Day time—r(${t}_{1}$) | 08:00–22:00 | 7.69 (¢/kWh) |

Night time—r(${t}_{2}$) | 22:00–08:22 | 5.42 (¢/kWh) |

Region 1 | ${\dot{Q}}_{load}<{\dot{Q}}_{st,ref}$ |

Region 2 | ${\dot{Q}}_{st,ref}<{\dot{Q}}_{load}<{\dot{Q}}_{hp,opt}$ |

Region 3 | ${\dot{Q}}_{hp,opt}<{\dot{Q}}_{load}<{\dot{Q}}_{st,ref}+{\dot{Q}}_{hp,opt}$ |

Region 4 | ${\dot{Q}}_{st,ref}+{\dot{Q}}_{hp,opt}<{\dot{Q}}_{load}<{\dot{Q}}_{st,ref}+{\dot{Q}}_{hp,ful}$ |

Region 5 | ${\dot{Q}}_{st,ref}+{\dot{Q}}_{hp,ful}<{\dot{Q}}_{load}$ |

**Table 8.**Comparison of simulation results with experiments according to control strategies for various load conditions.

Load | Performance | Experiment | Simulation | |||||
---|---|---|---|---|---|---|---|---|

Heat Pump Priority | Thermal Storage Priority | Region Control | Heat Pump Priority | Thermal Storage Priority | Region Control | |||

100% | Heating capacity | Heat pump | 0.65 | 0.61 | 0.62 | 0.62 | 0.60 | 0.61 |

Thermal storage | 0.35 | 0.39 | 0.38 | 0.38 | 0.40 | 0.39 | ||

Heat pump power consumption | Day | 0.6 | 0.57 | 0.57 | 0.56 | 0.57 | 0.57 | |

Night | 0.39 | 0.43 | 0.41 | 0.41 | 0.43 | 0.41 | ||

Total | 0.99 | 1.00 ^{1} | 0.98 | 0.97 | 1.00 ^{1} | 0.98 | ||

80% | Heating capacity | Heat pump | 0.62 | 0.43 | 0.49 | 0.6 | 0.44 | 0.48 |

Thermal storage | 0.19 | 0.38 | 0.32 | 0.21 | 0.37 | 0.33 | ||

Heat pump power consumption | Day | 0.49 | 0.37 | 0.39 | 0.46 | 0.38 | 0.39 | |

Night | 0.15 | 0.36 | 0.30 | 0.16 | 0.35 | 0.30 | ||

Total | 0.64 | 0.73 | 0.69 | 0.62 | 0.73 | 0.69 | ||

60% | Heating capacity | Heat pump | 0.62 | 0.26 | 0.39 | 0.61 | 0.23 | 0.41 |

Thermal storage | 0 | 0.36 | 0.23 | 0 | 0.38 | 0.20 | ||

Heat pump power consumption | Day | 0.45 | 0.25 | 0.32 | 0.48 | 0.24 | 0.33 | |

Night | 0 | 0.32 | 0.16 | 0 | 0.35 | 0.17 | ||

Total | 0.45 | 0.57 | 0.48 | 0.48 | 0.59 | 0.50 |

^{1}Non-dimensional reference; thermal storage priority method when the heating load 100%.

Parameter | Heat Pump Priority | Thermal Storage Priority | Region Control | Optimal Control |
---|---|---|---|---|

Day power consumption | 0.77 | 0.47 | 0.47 | 0.49 |

Night power consumption | 0.19 | 0.53 | 0.43 | 0.39 |

Total power consumption | 0.96 | 1.00 ^{2} | 0.90 | 0.88 |

Electricity cost | 1.08 | 1.00 ^{2} | 0.92 | 0.91 |

^{2}Non-dimensional reference; thermal storage priority method when the winter season.

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## Share and Cite

**MDPI and ACS Style**

Jung, W.; Kim, D.; Kang, B.H.; Chang, Y.S. Investigation of Heat Pump Operation Strategies with Thermal Storage in Heating Conditions. *Energies* **2017**, *10*, 2020.
https://doi.org/10.3390/en10122020

**AMA Style**

Jung W, Kim D, Kang BH, Chang YS. Investigation of Heat Pump Operation Strategies with Thermal Storage in Heating Conditions. *Energies*. 2017; 10(12):2020.
https://doi.org/10.3390/en10122020

**Chicago/Turabian Style**

Jung, Wangsik, Dongjun Kim, Byung Ha Kang, and Young Soo Chang. 2017. "Investigation of Heat Pump Operation Strategies with Thermal Storage in Heating Conditions" *Energies* 10, no. 12: 2020.
https://doi.org/10.3390/en10122020