# Energy Management of a Hybrid-Power Gas Engine-Driven Heat Pump

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Description of Energy Management on the Coaxial Parallel-Type HPGHP System

## 3. Model of the HPGHP System

#### 3.1. Model of the Engine

_{i}is model coefficient, e

_{i}is stochastic error, N is number of test points, A

_{m}is the coefficients of the regress equation.

#### 3.2. Model of the Motor [12]

## 4. The Energy Management Optimization Strategy of the HPGHP System

#### 4.1. The Comprehensive Efficiency of the HPGHP System

#### 4.1.1. The Comprehensive Efficiency of the HPGHP System under Charging Conditions

#### 4.1.2. The Comprehensive Efficiency of the HPGHP System under Discharging Conditions

#### 4.2. The Energy Management Optimization Strategy Model of the HPGHP System [15]

#### 4.2.1. The Energy Management Optimization Strategy Model of the HPGHP System under Charging Conditions

#### 4.2.2. The Energy Management Optimization Strategy Model of the HPGHP System under Discharging Conditions

#### 4.3. The Results of Energy Management Strategy

#### 4.3.1. The Energy Management Optimization Strategy of the HPGHP System under Charging Conditions

_{f}), and can be obtained from Equation (9), as shown in Equation (23):

_{1}(x) = −x ≤ 0

_{2}(x) = x/T

_{fmax}− 1 ≤ 0

_{3}(x) = |T

_{d}|/|T

_{dmin}| − 1 ≥ 0

_{dbase}, G

_{4}(x) = |T

_{d}|/|T

_{dmax}| − 1 ≤ 0

_{dbase}, G

_{4}(x) = |T

_{d}|ω/(9550|P

_{da}|) − 1 ≤ 0

_{fmax}is the maximum engine torque when the engine speed is ω, N.m. T

_{dmin}is the minimum allowed motor torque, N.m. T

_{dmax}is the maximum motor torque when the motor is operating continuously, N.m. P

_{da}is the actual maximum motor power when the SOC value is specific value. ω

_{dbase}is the basic motor speed when the SOC value is specific value, rad/s. This is expressed as follows:

_{da}= P

_{bmax}/η

_{d}η

_{n}

_{dbase}= 9550P

_{da}/T

_{dmax}

_{bmax}, which is measured by the performance tests of battery packs, is the continuous maximum charging power of battery packs and is the function of the SOC value.

Parameter | ${\mathbf{\eta}}_{\mathbf{b}}$ | ${\mathbf{\eta}}_{\mathbf{n}}$ | ${\mathbf{\eta}}_{\mathbf{dc}}$ | ${\mathbf{\eta}}_{\mathbf{df}}$ |
---|---|---|---|---|

Value range | 0.8–0.95 | 0.9–0.98 | 0.8–0.9 | 0.75–0.92 |

Selected value | 0.9 | 0.92 | 0.85 | 0.9 |

#### 4.3.2. The Energy Management Optimization Strategy of the HPGHP System under Discharging Conditions

_{1}(x) = −x ≤ 0

_{2}(x) = x/T

_{fmax}− 1 ≤ 0

_{3}(x) = T

_{y}− T

_{d}≤0

_{3}(x) = −T

_{d}≤ 0

_{m}

_{base}, G

_{4}(x) = T

_{d}/T

_{dmax}− 1 ≤ 0

_{m}

_{base}, G

_{4}(x) = T

_{d}ω/(9550P

_{ma}) − 1 ≤ 0

_{fmax}is the maximum engine torque when the engine speed is ω, N.m. P

_{ma}is the actual maximum motor power when the SOC value is specific value and P

_{ma}is obtained from the maximum power which the battery can discharge continuously, KW. ω

_{mbase}is the basic motor speed when the value of SOC is a specific value, rad/s. and is obtained from P

_{da}and the maximum motor torque, which is also the function of SOC expressed as follows:

_{bmax}, which is measured by the performance tests of battery packs, is the continuous maximum discharging power of battery packs and is the function of SOC, expressed as follows:

## 5. Control Strategy

_{min}, HPGHP operates in mode S and the engine drives the motor to charge the battery packs. When the SOC is more than the maximum discharge value SOC

_{max}, or the engine speed is not in the economical zone, HPGHP operates in mode M and the compressor is driven by the motor alone. When the SOC is within the specified interval (SOC

_{min}, SOC

_{max}) and the engine speed is in the economical zone, the operating modes of HPGHP are determined by the demanded torque, T. If the demanded torque is higher than the discharging torque limit, the HPGHP operates in mode L, then the engine and motor drive together and the engine operates in the economical zone. If the demanded torque is lower than the charging torque limit, the HPGHP operates in mode C, the engine drives the compressor and the generator to generate electricity. If the demand torque is between the charging torque limit and the discharging torque limit, the HPGHP operates in mode D, the engine operates in the economical zone that can meet full load of the HPGHP system and the motor stops operating.

Operation Mode | Boundary Conditions |
---|---|

mode D | ω_{low} < ω < ω_{high} and T_{low} < T < T_{high} |

mode C | ω_{low} < ω < ω_{high} and T < T_{low} and SOC < SOC_{high} |

mode L | ω_{low} < ω < ω_{high} and T_{high} < T and SOC > SOC_{low} |

mode M | ω > ω_{high} or ω < ω_{low} and SOC > SOC_{low} |

mode S | SOC < SOC_{low} |

## 6. Simulation and Experimental Comparison

_{f}). As the SOC value is around 0.6, the charging torque and discharging torque are fitted by the value of simulation, as is shown as Equations (27) and (28). The selection of the motor charging or discharging torque can meet the engine economic zone and take as big a value as possible in this paper.

**Figure 15.**The relation between the motor efficiency and compressor speed in different modes. (

**a**) In mode C; (

**b**) In mode L.

## 7. Conclusions

- (1)
- A comprehensive charging/discharging efficiency model and the energy management optimization strategy model is established. The results show that the comprehensive charging efficiency of the HPGHP system under charging/discharging conditions relates to the operating points, the engine and motor efficiency, respectively.
- (2)
- Different charging/discharging torque limits are obtained. The results show that the battery packs should be charged only when the required power is less than the charging power limit. In addition, the discharging torque limits become higher and the charging torque limits become lower when the SOC value becomes lower. The motor starts running only when the demand torque or power becomes larger at this moment.
- (3)
- In the HPGHP system operation process, during 3600 s of run-time, the SOC value of battery packs ranges between 0.58 and 0.705, the fuel consumption rate reaches a minimum value of approximately 291.3 g/(kW h) when the compressor speed is 1550 rpm in mode D and ranges between 291–330 g/(kW h), the engine thermal efficiency and comprehensive efficiency reach a maximum value of approximately 0.2727/0.2648 when the compressor speed is 1575 rpm/1475 rpm in mode D, respectively and ranges between 0.2400 and 0.2750, 0.2300 and 0.2700, respectively. In general, the fuel consumption rate reach a minimum value of approximately 291.3 g/(kW h) when the compressor speed is nearly 1550 rpm in mode D, the engine thermal efficiency and comprehensive efficiency reach maximum values of approximately 0.2727/0.2648 when the compressor speed is 1575 rpm/1475 rpm, respectively, in mode D. In addition, the motor efficiency can be maintained above 0.85 in either mode. Finally, because of the application of the gas engine economical zone control strategy to the HPGHP system, the fuel consumption rate is about 1.6% less than that analyzed in Wang et al. [9].

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

η_{f} | the thermal efficiency of the gas engine |

T_{f} | the torque of the gas engine (Nm) |

ω_{f} | the speed of the gas engine (rpm) |

T_{d} | the torque of the motor (Nm) |

ω_{d} | the speed of the motor (rpm) |

η_{d} | the thermal efficiency of the motor |

η_{dc} | the motor charging efficiency |

η_{df} | the motor discharging efficiency |

η_{b} | transmission efficiency (%) |

η_{n} | inverter efficiency (%) |

$\overline{\text{\eta}}$ | average comprehensive efficiency (%) |

P_{q} | gas output power (KW) |

P_{f} | the output power of the engine (KW) |

P_{dc} | the battery charging power (KW) |

P_{d} | the motor input power (KW) |

P_{df} | the battery discharging power (KW) |

P_{d}’ | the motor output power (KW) |

ω | the speed of the compressor (rpm) |

P_{y} | input power of the compressor (KW) |

P_{qd} | gas bottle equivalent input power of the battery (KW) |

## Subscripts

y | the compressor |

dc | the condition of charging |

df | the condition of discharging |

f | the engine |

d | the motor |

max | the maximum value |

min | the minimum value |

η | efficiency (%) |

T | the torque (Nm) |

ω | the speed (rpm) |

## Abbreviations

COP | coefficient of performance |

GHP | gas engine heat pump |

HPGHP | hybrid-power gas engine heat pump |

SOC | the state of charge |

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## Share and Cite

**MDPI and ACS Style**

Meng, Q.; Cai, L.; Ji, W.; Yan, J.; Zhang, T.; Zhang, X.
Energy Management of a Hybrid-Power Gas Engine-Driven Heat Pump. *Energies* **2015**, *8*, 11254-11275.
https://doi.org/10.3390/en81011254

**AMA Style**

Meng Q, Cai L, Ji W, Yan J, Zhang T, Zhang X.
Energy Management of a Hybrid-Power Gas Engine-Driven Heat Pump. *Energies*. 2015; 8(10):11254-11275.
https://doi.org/10.3390/en81011254

**Chicago/Turabian Style**

Meng, Qingkun, Liang Cai, Wenxiu Ji, Jie Yan, Tao Zhang, and Xiaosong Zhang.
2015. "Energy Management of a Hybrid-Power Gas Engine-Driven Heat Pump" *Energies* 8, no. 10: 11254-11275.
https://doi.org/10.3390/en81011254