This article uses BIM technology to simulate HVAC in a commercial building. And use fractional differential equations to verify the set temperature, humidity, and other related parameters. The experiment takes an air-conditioned room model as the research object and uses the thermodynamic characteristics to establish a dynamic mathematical model of differential equations. Research shows that the multiple electric heat pump equipment aggregation groups discussed in this article are a good resource for user-side demand response. The air-side flow rate disturbance of the building HVAC has the greatest impact on the heat transfer of the surface cooler. As the air velocity increases, the rate of increase in heat exchange will decrease.

#### Keywords

- Fractional differential equation
- BIM
- Temperature control load
- Electric heat pump equipment
- Modeling method
- Air conditioning energy saving

#### MSC 2010

- 34A08

Demand response is mainly to adjust electricity consumption patterns through electricity prices or incentive measures to change the behavior of humans using the equipment. The household temperature control load has good thermal energy storage characteristics. It accounts for 40% to 50% of residential electricity load and has gradually become a key research object of demand response [1]. As a typical RTCL (residential thermostatically controlled loads), an electric heat pump is a heating form of HVAC loads. It is an important heating load gradually promoted in the south. With the continuous in-depth development of intelligent power distribution technology, electric heat pump equipment's demand response control potential is increasingly becoming a research hotspot.

The electric heat pump load modeling method and control strategy are the basis of the research on its demand response mechanism. At present, there are mainly two types of methods for the model study of air-conditioning load. One is the “top-down” modeling method. It performs overall modeling and load identification and prediction for air conditioning load groups [2]. These models are widely used in large power grid electromechanical transient and small disturbance simulation and analysis. The “top-down” load modeling method mainly considers the overall equivalent model of the air-conditioning load group, so another “bottom-up” modeling method has gradually gained attention. This method considers the comprehensive influence of various factors such as the basic operating mechanism of household electric heat pump equipment, thermodynamic dynamic properties, and human use behavior. It constructs a load model based on the physical mechanism. At present, in the demand response control technology, the equivalent thermodynamic parameter ETP is mainly used for modeling, and the temperature dynamics are described in the form of differential equations.

Academia has gradually developed an identification control algorithm based on the Fokker Planck equation in the control strategy. This paper adopts the ETP model in the form of second-order differential equations to model the thermoelectric coupling of electric heat pump equipment and constructs a load demand model formed by aggregating multiple electric heat pump loads. On this basis, four electric heat pump load control strategies are designed and evaluated [3]. We analyzed their respective characteristics and gave relevant control strategies that can cut peaks and fill valleys and increase the load rate of the power grid. The aggregation group of multiple electric heat pump equipment discussed in this article is a good resource for user-side demand response.

HVAC (heating ventilation and air condition) is comprehensive air conditioning equipment. It is used for heating and cooling, as well as exhaust air. The electric heat pump is its heating form, and the academic circles mainly use the second-order differential equation ETP model to describe [4]. We use the indoor temperature regulated by the electric heat pump and the indoor material temperature change as the two-state variables observed in the ETP model for research. The specific differential equation of the two-prime model is

_{a}_{m}_{a}_{m}_{o}_{a}_{m}

The most important feature of this kind of equipment thermodynamic dynamic model based on the physical mechanism is that the corresponding temperature change and the state of equipment consumption electric power have a one-to-one correspondence function [5]. The thermoelectric coupling model is

_{op}_{rated}_{AC}

_{s}_{+}, _{−} respectively set the temperature value and the upper and lower limits of temperature adjustment for HVAC work.

Simulation parameters of typical electric heat pumps.

Parameter | Describe | Typical value |
---|---|---|

_{a} |
Standby indoor air thermal resistance | 2°C/kW |

Indoor comprehensive heat capacity | 10(kW·)/°C | |

_{m} |
Indoor material heat capacity | 75%C |

_{a} |
Indoor air heat capacity | 25%C |

_{m} |
Material thermal resistance in standby room | 0.1°C/kW |

The standard deviation of thermodynamic parameter distribution | 0.2 | |

_{s} |
Temperature setpoint | 20°C |

Temperature adjustment range | 2°C | |

_{AC} |
Electric heat pump conversion efficiency | 0.3 |

Δ |
Sampling interval | 1min |

_{n} |
The standard deviation of white noise εk in indoor temperature measurement | 0.01°C·s^{−1}/2 |

_{0} |
Initial simulation setting room temperature value | 19°C |

Because of the regional distribution of air-conditioning equipment, the habit of users, and other factors, the thermodynamic parameters of group _{a}_{m}_{a}_{m}

_{AC}_{AC}

The control of the electric heat pump equipment group is based on the curve (baseline) of its normal operation [7]. Changing the temperature setting of the electric heat pump can change the output of the electric heat pump to achieve the purpose of transforming its load curve (Figure 4). It can be seen that increasing the temperature setting of the electric heat pump can change the output of the electric heat pump and raise the overall power level of the electric heat pump equipment group.

This definition is used to measure the load shedding ability of the control strategy during the peak load period of the power system:

_{curtailment}_{curtailment,t}_{origin,t}_{t}_{b}_{e}

The daily average load of the electric heat pump equipment group is used to measure the energy consumption of the control strategy:

_{average}_{t}

The daily load rate of the electric heat pump equipment group is used to measure the severity of the new load peak generated by the control strategy:

The cumulative duration that the indoor temperature is lower than the user's temperature requirement is used to reflect the influence of the control strategy on the user's thermal comfort [8]. In addition, because the user's acceptance range for room temperature is roughly ±2°C based on the temperature setting, the situation where the room temperature is lower than the original temperature setting by 2°C is regarded as a temperature violation. The formula for calculating the duration of temperature violation is

_{violation}_{n,t}_{n,t}

The index values of the four electric heat pump equipment group control strategies proposed in this section in the corresponding calculation examples are shown in Table 2. It can be seen from Table 2 that various control strategies have different performances when the change of the temperature setting value is 2°C. The constant set value strategy is the state of the load working normally. It serves as a benchmark to measure the effectiveness of other strategies [9]. The last three strategies can reduce peak load to a certain extent from reducing peak load. Among them, the ability of pre-heating strategy is the strongest, followed by the ability of peak shaving strategy, and the ability to improve pre-heating strategy is the weakest. The pre-heating strategy has the strongest peak-shaving ability because it stores much heat energy in advance. The temperature setting value is lowered during peak hours so that only a few electric heat pumps need to be turned on during peak hours. The reason for the relatively weakest peak-shaving ability of the improved pre-heating strategy is that its temperature setting is gradual. This process makes the stored heat energy before the peak period less than the improved pre-heating strategy before the sudden change of the temperature set point. The gradual change of the temperature setting value during peak hours is also not conducive to shutting down the electric heat pump load quickly.

Evaluation results of control strategy of electric heat pump equipment group.

Control Strategy | _{curtailment} |
_{average} |
APR/% | _{violation} |
---|---|---|---|---|

Constant set value | 0 | 2.309 | 66.93 | 0 |

Peak clipping | 27.38 | 2.266 | 37.76 | 1.51 |

Preheat | 33.22 | 2.336 | 38.93 | 0.52 |

Improve advance heating | 14.28 | 2.32 | 47.98 | 0.51 |

From the perspective of energy consumption, it is found that the peak-shaving strategy has the lowest energy consumption because it cuts the load and reduces the total energy consumption [10]. The energy consumption of the pre-heating load before and after the improvement is greater than the peak shaving strategy and the constant set value strategy. This is because the pre-heating strategy heats the indoor air to a higher temperature before peak hours, which intensifies the rate of heat dissipation.

From the perspective of the load rate of the electric heat pump equipment group, the last three control strategies all reduce the load rate to varying degrees. This shows that new load peaks (or load rebounds caused by pre-heating) have been generated during peak shaving. The load rate of the improved pre-heating strategy is higher than that of the peak-shaving strategy and the pre-improved pre-heating strategy, which shows that its gradual temperature setting can effectively alleviate the problem of new load peaks to a certain extent.

It can be seen from the average temperature violation duration that the peak-shaving strategy has the most serious damage to user comfort. The pre-heating strategy can better ensure user comfort even when the temperature is lowered during peak hours because the heat energy is stored in advance [11]. This is less harmful to the user's comfort. Improved advance heating strategy temperature setting changes smoothly. This has the least damage to the user's comfort. The above four control strategies have their characteristics, advantages, and disadvantages. In reality, select the appropriate control strategy according to the needs. For example, the pre-heating strategy has the strongest peak-shaving ability, so it can be considered when many peak load reductions are required. Improving the pre-heating strategy has less damage to user comfort and less load rebound. This can be selected when the demand for peak clipping is low, and the user's comfort priority is higher. Although the peak-shaving strategy will cause more serious load rebound and user comfort damage, it does not need to be heated in advance and has a strong load-shaving ability. Therefore, this model can be used in scenarios where the load needs to be temporarily reduced.

The “top-down” method performs equivalent modeling of the overall dynamic mechanism of the load or the interference of external factors. With the continuous in-depth development of smart power distribution technology, traditional models cannot reflect the effects imposed by user-side demand response control strategies. This paper uses the second-order differential equation form of thermodynamic mechanism to model the electric heat pump equipment. We built a load demand model that aggregates loads of multiple electric heat pumps. On this basis, four electric heat pump load control strategies are designed and evaluated, and their characteristics are analyzed. The aggregation group of multiple electric heat pump equipment discussed in this article is a good resource for user-side demand response. Various system goals can be achieved through proper control, and it has a wide range of engineering application prospects.

#### Simulation parameters of typical electric heat pumps.

Parameter | Describe | Typical value |
---|---|---|

_{a} |
Standby indoor air thermal resistance | 2°C/kW |

Indoor comprehensive heat capacity | 10(kW·)/°C | |

_{m} |
Indoor material heat capacity | 75%C |

_{a} |
Indoor air heat capacity | 25%C |

_{m} |
Material thermal resistance in standby room | 0.1°C/kW |

The standard deviation of thermodynamic parameter distribution | 0.2 | |

_{s} |
Temperature setpoint | 20°C |

Temperature adjustment range | 2°C | |

_{AC} |
Electric heat pump conversion efficiency | 0.3 |

Δ |
Sampling interval | 1min |

_{n} |
The standard deviation of white noise εk in indoor temperature measurement | 0.01°C·s^{−1}/2 |

_{0} |
Initial simulation setting room temperature value | 19°C |

#### Evaluation results of control strategy of electric heat pump equipment group.

Control Strategy | _{curtailment} |
_{average} |
APR/% | _{violation} |
---|---|---|---|---|

Constant set value | 0 | 2.309 | 66.93 | 0 |

Peak clipping | 27.38 | 2.266 | 37.76 | 1.51 |

Preheat | 33.22 | 2.336 | 38.93 | 0.52 |

Improve advance heating | 14.28 | 2.32 | 47.98 | 0.51 |

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